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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1807.01997">arXiv:1807.01997</a> <span> [<a href="https://arxiv.org/pdf/1807.01997">pdf</a>, <a href="https://arxiv.org/ps/1807.01997">ps</a>, <a href="https://arxiv.org/format/1807.01997">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.7546/jgsp-46-2017-1-24">10.7546/jgsp-46-2017-1-24 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Is spacetime as physical as is space? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1807.01997v1-abstract-short" style="display: inline;"> Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a congruence of reference trajectories, defines a physical space. The points of that space are formally defined to be the world lines of the congruence. That space can… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.01997v1-abstract-full').style.display = 'inline'; document.getElementById('1807.01997v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1807.01997v1-abstract-full" style="display: none;"> Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a congruence of reference trajectories, defines a physical space. The points of that space are formally defined to be the world lines of the congruence. That space can be endowed with a natural structure of 3-D differentiable manifold, thus giving rise to a simple notion of spatial tensor --- namely, a tensor on the space manifold. The second question is: does the geometric structure of the spacetime determine the physics, in particular, does it determine its relativistic or preferred-frame character? We find that it does not, for different physics (either relativistic or not) may be defined on the same spacetime structure --- and also, the same physics can be implemented on different spacetime structures. Keywords: Affine space; classical mechanics; special relativity; relativistic gravity; reference fluid. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.01997v1-abstract-full').style.display = 'none'; document.getElementById('1807.01997v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 July, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 70A05; 70B05; 83A05; 83D05 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Journal of Geometry and Symmetry in Physics, Vol. 46, pp. 1-24 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1510.02616">arXiv:1510.02616</a> <span> [<a href="https://arxiv.org/pdf/1510.02616">pdf</a>, <a href="https://arxiv.org/ps/1510.02616">ps</a>, <a href="https://arxiv.org/format/1510.02616">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Classical Physics">physics.class-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1155/2016/9679460">10.1155/2016/9679460 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the definition of energy for a continuum, its conservation laws, and the energy-momentum tensor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1510.02616v3-abstract-short" style="display: inline;"> We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contain… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.02616v3-abstract-full').style.display = 'inline'; document.getElementById('1510.02616v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1510.02616v3-abstract-full" style="display: none;"> We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contains two local conservation equations of the same kind as before. We show that both of these equations depend on the reference frame, and that, however, they can be given a rigorous meaning. Then we review the definitions of the canonical and Hilbert energy-momentum tensors from a Lagrangian through the principle of stationary action in a general spacetime. Using relatively elementary mathematics, we prove precise results regarding the definition of the Hilbert tensor field, its uniqueness, and its tensoriality. We recall the meaning of its covariant conservation equation. We end with a proof of uniqueness of the energy density and flux, when both depend polynomially of the fields. Keywords: energy conservation; conservation equation; special relativity; general relativity; Hilbert tensor; variational principle <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.02616v3-abstract-full').style.display = 'none'; document.getElementById('1510.02616v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 September, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 October, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 pages in 12pt article format. Published version is Open Access at Publisher (see DOI below). This version (V3) is a review article that exposes in detail the results of V2 and also presents results not discussed there. V1 and V2 are successive versions of a conference talk. Sect. 3.5 of V2 contains results which are not there in V3</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Adv. Math. Phys. Vol. 2016 (2016), Article ID 9679460, 15 pages </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1502.04085">arXiv:1502.04085</a> <span> [<a href="https://arxiv.org/pdf/1502.04085">pdf</a>, <a href="https://arxiv.org/ps/1502.04085">ps</a>, <a href="https://arxiv.org/format/1502.04085">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1742-6596/626/1/012030">10.1088/1742-6596/626/1/012030 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1502.04085v1-abstract-short" style="display: inline;"> The definition of the Hamiltonian operator H for a general wave equa-tion in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation involves a gauge choice and the gauge change is time-dependent, H as an operator depends on the gauge choice. This dependence extends to the energy operator E, which… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1502.04085v1-abstract-full').style.display = 'inline'; document.getElementById('1502.04085v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1502.04085v1-abstract-full" style="display: none;"> The definition of the Hamiltonian operator H for a general wave equa-tion in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation involves a gauge choice and the gauge change is time-dependent, H as an operator depends on the gauge choice. This dependence extends to the energy operator E, which is the Hermitian part of H. We distinguish between this ambiguity issue of E and the one that occurs due to a mere change of the "represen-tation" (e.g. transforming the Dirac wave function from the "Dirac representation" to a "Foldy-Wouthuysen representation"). We also assert that the energy operator ought to be well defined in a given ref-erence frame at a given time, e.g. by comparing the situation for this operator with the main features of the energy for a classical Hamilto-nian particle. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1502.04085v1-abstract-full').style.display = 'none'; document.getElementById('1502.04085v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 February, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Text of a talk given at the DICE2014 Workshop (Castiglioncello (Livorno), Italy). Submitted to the Proceedings (H.T. Elze et al., eds.). in Seventh International Workshop DICE2014: Spacetime - Matter - Quantum Mechanics, Sep 2014, Castiglioncello (Provincia di Livorno), Italy</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. Conf. Ser., Vol. 626, 012030 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1312.6707">arXiv:1312.6707</a> <span> [<a href="https://arxiv.org/pdf/1312.6707">pdf</a>, <a href="https://arxiv.org/ps/1312.6707">ps</a>, <a href="https://arxiv.org/format/1312.6707">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Physics">physics.gen-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Comment on "Spin in an arbitrary gravitational field" arXiv:1308.4552 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1312.6707v1-abstract-short" style="display: inline;"> The authors of that work [Phys. Rev. D 88, 084014 (2013)], arXiv:1308.4552, derive quantum-mechanical equations valid for the covariant Dirac equation by restricting the choice of the tetrad field through the use of the "Schwinger gauge". Yet it has been shown previously that this gauge leaves space for a physical ambiguity of the Hamiltonian operator. It is shown here precisely how this ambiguity… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1312.6707v1-abstract-full').style.display = 'inline'; document.getElementById('1312.6707v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1312.6707v1-abstract-full" style="display: none;"> The authors of that work [Phys. Rev. D 88, 084014 (2013)], arXiv:1308.4552, derive quantum-mechanical equations valid for the covariant Dirac equation by restricting the choice of the tetrad field through the use of the "Schwinger gauge". Yet it has been shown previously that this gauge leaves space for a physical ambiguity of the Hamiltonian operator. It is shown here precisely how this ambiguity occurs with their settings. There is another ambiguity in the Foldy-Wouthuysen Hamiltonian, for the time-dependent case which is relevant here. However, their equations of motion for classical spinning particles are unambiguous. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1312.6707v1-abstract-full').style.display = 'none'; document.getElementById('1312.6707v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 December, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1310.8128">arXiv:1310.8128</a> <span> [<a href="https://arxiv.org/pdf/1310.8128">pdf</a>, <a href="https://arxiv.org/ps/1310.8128">ps</a>, <a href="https://arxiv.org/format/1310.8128">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> On reference frames and the definition of space in a general spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1310.8128v1-abstract-short" style="display: inline;"> First, we review local concepts defined previously. A (local) reference frame $\mathrm{F}$ can be defined as an equivalence class of admissible spacetime charts (coordinate systems) having a common domain $\mathrm{U}$ and exchanging by a spatial coordinate change. The associated (local) physical space is made of the world lines having constant space coordinates in any chart of the class. Second, w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1310.8128v1-abstract-full').style.display = 'inline'; document.getElementById('1310.8128v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1310.8128v1-abstract-full" style="display: none;"> First, we review local concepts defined previously. A (local) reference frame $\mathrm{F}$ can be defined as an equivalence class of admissible spacetime charts (coordinate systems) having a common domain $\mathrm{U}$ and exchanging by a spatial coordinate change. The associated (local) physical space is made of the world lines having constant space coordinates in any chart of the class. Second, we introduce new, global concepts. The data of a non-vanishing global vector field $\,v\,$ defines a global "reference fluid". The associated global physical space is made of the maximal integral curves of that vector field. Assume that, in any of the charts which make some reference frame $\mathrm{F}$: (i) any of those integral curves $l$ has constant space coordinates $x^j$, and (ii) the mapping $l\mapsto (x^j)$ is one-to-one. In that case, the local space can be identified with a part (an open subset) of the global space. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1310.8128v1-abstract-full').style.display = 'none'; document.getElementById('1310.8128v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 October, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages. Text of a talk given at the Third International Conference on Theoretical Physics "Theoretical Physics and its Applications", Moscow, June 24-28, 2013</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Proc. Int. Conf. "Theoretical Physics and its new Applications" (T.F. Kamalov, ed.), Moscow Institute of Physics & Technology (2014), pp. 71-76 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.5584">arXiv:1302.5584</a> <span> [<a href="https://arxiv.org/pdf/1302.5584">pdf</a>, <a href="https://arxiv.org/ps/1302.5584">ps</a>, <a href="https://arxiv.org/format/1302.5584">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s10773-013-1717-x">10.1007/s10773-013-1717-x <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the non-uniqueness problem of the covariant Dirac theory and the spin-rotation coupling </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.5584v2-abstract-short" style="display: inline;"> Gorbatenko & Neznamov [arXiv:1301.7599] recently claimed the absence of the title problem. In this paper, the reason for that problem is reexplained by using the notions of a unitary transformation and of the mean value of an operator, invoked by them. Their arguments actually aim at proving the uniqueness of a particular prescription for solving this problem. But that prescription is again shown… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.5584v2-abstract-full').style.display = 'inline'; document.getElementById('1302.5584v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.5584v2-abstract-full" style="display: none;"> Gorbatenko & Neznamov [arXiv:1301.7599] recently claimed the absence of the title problem. In this paper, the reason for that problem is reexplained by using the notions of a unitary transformation and of the mean value of an operator, invoked by them. Their arguments actually aim at proving the uniqueness of a particular prescription for solving this problem. But that prescription is again shown non-unique. Two Hamiltonians in the same reference frame in a Minkowski spacetime, only one of them including the spin-rotation coupling term, are proved to be physically non-equivalent. This confirms that the reality of that coupling should be checked experimentally. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.5584v2-abstract-full').style.display = 'none'; document.getElementById('1302.5584v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 June, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages. V2: Version to appear in Int. J. Theor. Phys.: Details about the (gross) inequivalence of the Hamiltonians with either the inertial tetrad or the rotating one on pp. 11-12. Added Appendix proving that, for the (standard) covariant Dirac equation, the mean values of the energy can not be shifted by a constant after a smooth change of the tetrad field. Added Footnote 2 on p. 4</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Int. J. Theor. Phys., vol. 52, No. 11, pp. 4032-4044 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1211.1855">arXiv:1211.1855</a> <span> [<a href="https://arxiv.org/pdf/1211.1855">pdf</a>, <a href="https://arxiv.org/ps/1211.1855">ps</a>, <a href="https://arxiv.org/format/1211.1855">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s10773-014-2006-z">10.1007/s10773-014-2006-z <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Should there be a spin-rotation coupling for a Dirac particle? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1211.1855v2-abstract-short" style="display: inline;"> It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We compute the energy operator in the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1211.1855v2-abstract-full').style.display = 'inline'; document.getElementById('1211.1855v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1211.1855v2-abstract-full" style="display: none;"> It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We compute the energy operator in the inertial and the rotating frame, using three tetrad fields: one for each of two frameworks proposed to select the tetrad field so as to solve this non-uniqueness problem, and one proposed by Ryder. We find that Mashhoon's term is there if the tetrad rotates as does the reference frame --- but then it is also there in the energy operator for the inertial frame. In fact, the Dirac Hamiltonian operators in two reference frames in relative rotation, but corresponding to the same tetrad field, differ only by the angular momentum term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field must be selected in a specific way for each reference frame. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1211.1855v2-abstract-full').style.display = 'none'; document.getElementById('1211.1855v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 September, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 November, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">29 pages in standard 12pt. V2: Introduction reinforced. New Section 3 on the dependences of the Hamiltonian on the reference frame and on the tetrad field. New references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Int. J. Theor. Phys., Vol. 53, No. 6, pp. 1993-2013 (2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1209.5738">arXiv:1209.5738</a> <span> [<a href="https://arxiv.org/pdf/1209.5738">pdf</a>, <a href="https://arxiv.org/ps/1209.5738">ps</a>, <a href="https://arxiv.org/format/1209.5738">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Summary of a non-uniqueness problem of the covariant Dirac theory and of two solutions of it </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1209.5738v2-abstract-short" style="display: inline;"> We present a summary of: 1) the non-uniqueness problem of the Hamiltonian and energy operators associated, in any given coordinate system, with the generally-covariant Dirac equation; 2) two different ways to restrict the gauge freedom so as to solve that problem; 3) the application of these two ways to the case of a uniformly rotating reference frame in Minkowski spacetime: we find that a spin-ro… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1209.5738v2-abstract-full').style.display = 'inline'; document.getElementById('1209.5738v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1209.5738v2-abstract-full" style="display: none;"> We present a summary of: 1) the non-uniqueness problem of the Hamiltonian and energy operators associated, in any given coordinate system, with the generally-covariant Dirac equation; 2) two different ways to restrict the gauge freedom so as to solve that problem; 3) the application of these two ways to the case of a uniformly rotating reference frame in Minkowski spacetime: we find that a spin-rotation coupling term is there only with one of these two ways. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1209.5738v2-abstract-full').style.display = 'none'; document.getElementById('1209.5738v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 October, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 September, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages in standard 12pt. v2: misprint fixed in Eq (20). Text of a talk given at the 14th International Conference on Geometry, Integrability and Quantization (Varna, Bulgaria, June 2012)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Proc. Int. Conf. "Geometry, Integrability and Quantization XIV", ed. by Iva茂lo Mladenov, Andrei Ludu & Akira Yoshioka; Avangard Prima, Sofia (2013), pp 48-60 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1205.3386">arXiv:1205.3386</a> <span> [<a href="https://arxiv.org/pdf/1205.3386">pdf</a>, <a href="https://arxiv.org/ps/1205.3386">ps</a>, <a href="https://arxiv.org/format/1205.3386">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0219887813500278">10.1142/S0219887813500278 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A simpler solution of the non-uniqueness problem of the covariant Dirac theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1205.3386v4-abstract-short" style="display: inline;"> Although the standard generally-covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the va… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1205.3386v4-abstract-full').style.display = 'inline'; document.getElementById('1205.3386v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1205.3386v4-abstract-full" style="display: none;"> Although the standard generally-covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isotropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1205.3386v4-abstract-full').style.display = 'none'; document.getElementById('1205.3386v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 September, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 February, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">32 pages in 12pt article. V4: Matches exactly with published version: Theorem 1 corrected (physical relevance unchanged)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Int. J. Geom. Methods Mod. Phys., Vol. 10, 1350027 (2013) [24 pages] </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1109.6649">arXiv:1109.6649</a> <span> [<a href="https://arxiv.org/pdf/1109.6649">pdf</a>, <a href="https://arxiv.org/ps/1109.6649">ps</a>, <a href="https://arxiv.org/format/1109.6649">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Classical-quantum correspondence and wave packet solutions of the Dirac equation in a curved spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1109.6649v1-abstract-short" style="display: inline;"> The idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar 蠅$ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave equation. We derive the expression of $H$ in a curved spacetime with an electromagnetic field. Then we derive the Dirac equation from factorizing the polynomial dispe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1109.6649v1-abstract-full').style.display = 'inline'; document.getElementById('1109.6649v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1109.6649v1-abstract-full" style="display: none;"> The idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar 蠅$ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave equation. We derive the expression of $H$ in a curved spacetime with an electromagnetic field. Then we derive the Dirac equation from factorizing the polynomial dispersion equation corresponding with $H$. Conversely, summarizing a recent work, we implement the geometrical optics approximation into a canonical form of the Dirac Lagrangian. Euler-Lagrange equations are thus obtained for the amplitude and phase of the wave function. From them, one is led to define a 4-velocity field which obeys exactly the classical equation of motion. The complete de Broglie relations are then derived exact equations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1109.6649v1-abstract-full').style.display = 'none'; document.getElementById('1109.6649v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 September, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages (standard 12pt). Text of a talk given at the "Geometry, Integrability & Quantization" Conference, Varna (Bulgaria), June 2011</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. of Geometry & Symmetry in Physics 24 (2011) pp. 77-88 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1107.4556">arXiv:1107.4556</a> <span> [<a href="https://arxiv.org/pdf/1107.4556">pdf</a>, <a href="https://arxiv.org/ps/1107.4556">ps</a>, <a href="https://arxiv.org/format/1107.4556">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1002/andp.201100166">10.1002/andp.201100166 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A solution of the non-uniqueness problem of the Dirac Hamiltonian and energy operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1107.4556v2-abstract-short" style="display: inline;"> In a general spacetime, the possible choices for the field of orthonormal tetrads lead (in standard conditions) to equivalent Dirac equations. However, the Hamiltonian operator is got from rewriting the Dirac equation in a form adapted to a particular reference frame, or class of coordinate systems. That rewriting does not commute with changing the tetrad field $(u_伪)$. The data of a reference fra… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1107.4556v2-abstract-full').style.display = 'inline'; document.getElementById('1107.4556v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1107.4556v2-abstract-full" style="display: none;"> In a general spacetime, the possible choices for the field of orthonormal tetrads lead (in standard conditions) to equivalent Dirac equations. However, the Hamiltonian operator is got from rewriting the Dirac equation in a form adapted to a particular reference frame, or class of coordinate systems. That rewriting does not commute with changing the tetrad field $(u_伪)$. The data of a reference frame F fixes a four-velocity field $v$, and also fixes a rotation-rate field $\Mat惟$. It is natural to impose that $u_0=v$. We show that then the spatial triad $(u_p)$ can only be rotating w.r.t. F, and that the title problem is solved if one imposes that the corresponding rotation rate $\Mat螢$ be equal to $\Mat惟$ - or also, if one imposes that $\Mat螢=\Mat{0}$. We also analyze other proposals which aimed at solving the title problem. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1107.4556v2-abstract-full').style.display = 'none'; document.getElementById('1107.4556v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 July, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 July, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">32 pages (standard 12pt), including appendices. v2: a minor new remark on pp. 29-30</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Ann. Phys. (Berlin) 523, No. 12, 1008-1028 (2011) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1103.3201">arXiv:1103.3201</a> <span> [<a href="https://arxiv.org/pdf/1103.3201">pdf</a>, <a href="https://arxiv.org/ps/1103.3201">ps</a>, <a href="https://arxiv.org/format/1103.3201">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s13538-012-0111-0">10.1007/s13538-012-0111-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1103.3201v4-abstract-short" style="display: inline;"> One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1103.3201v4-abstract-full').style.display = 'inline'; document.getElementById('1103.3201v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1103.3201v4-abstract-full" style="display: none;"> One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1103.3201v4-abstract-full').style.display = 'none'; document.getElementById('1103.3201v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 March, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem 2</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Brazilian Journal of Physics 43, No. 1-2, 64-77 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1012.2327">arXiv:1012.2327</a> <span> [<a href="https://arxiv.org/pdf/1012.2327">pdf</a>, <a href="https://arxiv.org/ps/1012.2327">ps</a>, <a href="https://arxiv.org/format/1012.2327">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0219887812500260">10.1142/S0219887812500260 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Four-vector vs. four-scalar representation of the Dirac wave function </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1012.2327v2-abstract-short" style="display: inline;"> In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar茅 group. This is not an option in a curved spacetime. Therefore, in the equation proposed independently by Fock and Weyl, the four complex components of the Dirac wave function transform as scalars under a general coordinate transformation. Recent work has shown… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.2327v2-abstract-full').style.display = 'inline'; document.getElementById('1012.2327v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1012.2327v2-abstract-full" style="display: none;"> In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar茅 group. This is not an option in a curved spacetime. Therefore, in the equation proposed independently by Fock and Weyl, the four complex components of the Dirac wave function transform as scalars under a general coordinate transformation. Recent work has shown that a covariant complex four-vector representation is also possible. Using notions of vector bundle theory, we describe these two representations in a unified framework. We prove theorems that relate together the different representations and the different choices of connections within each representation. As a result, either of the two representations can account for a variety of inequivalent, linear, covariant Dirac equations in a curved spacetime that reduce to the original Dirac equation in a Minkowski spacetime. In particular, we show that the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the covariant Dirac equation for a complex four-vector wave function. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.2327v2-abstract-full').style.display = 'none'; document.getElementById('1012.2327v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 October, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 December, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages (standard 12pt). v2: version accepted for publication in Int. J. Geom. Meth. Mod. Phys. Some emphasis and a clarification in Sect. 2.1. The Appendix now proves that the complex tangent bundle is a spinor bundle according to precisely the definition given in Sect. 2.1. Proof of the main Theorem 2 made easier to follow</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Int. J. Geom. Meth. Mod. Phys., Vol. 9, 1250026 (2012) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1011.6286">arXiv:1011.6286</a> <span> [<a href="https://arxiv.org/pdf/1011.6286">pdf</a>, <a href="https://arxiv.org/ps/1011.6286">ps</a>, <a href="https://arxiv.org/format/1011.6286">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1742-6596/306/1/012061">10.1088/1742-6596/306/1/012061 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Representations of the Dirac wave function in a curved spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1011.6286v1-abstract-short" style="display: inline;"> The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove theorems that relate together the different representations and the different choices of connections. In particular, the standard Dirac equation in a curved spa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1011.6286v1-abstract-full').style.display = 'inline'; document.getElementById('1011.6286v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1011.6286v1-abstract-full" style="display: none;"> The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove theorems that relate together the different representations and the different choices of connections. In particular, the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the Dirac equation for a vector wave function, in the same spacetime. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1011.6286v1-abstract-full').style.display = 'none'; document.getElementById('1011.6286v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 November, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages (standard 12pt article). Text of a talk given at DICE2010: "Space-Time-Matter - current issues in quantum mechanics and beyond" (Castiglioncello, Italy, September 13-17, 2010)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Phys.Conf.Ser.306:012061,2011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1003.3521">arXiv:1003.3521</a> <span> [<a href="https://arxiv.org/pdf/1003.3521">pdf</a>, <a href="https://arxiv.org/ps/1003.3521">ps</a>, <a href="https://arxiv.org/format/1003.3521">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0219887811005051">10.1142/S0219887811005051 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> General reference frames and their associated space manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1003.3521v2-abstract-short" style="display: inline;"> We propose a formal definition of a general reference frame in a general spacetime, as an equivalence class of charts. This formal definition corresponds with the notion of a reference frame as being a (fictitious) deformable body, but we assume, moreover, that the time coordinate is fixed. This is necessary for quantum mechanics, because the Hamiltonian operator depends on the choice of the time… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.3521v2-abstract-full').style.display = 'inline'; document.getElementById('1003.3521v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1003.3521v2-abstract-full" style="display: none;"> We propose a formal definition of a general reference frame in a general spacetime, as an equivalence class of charts. This formal definition corresponds with the notion of a reference frame as being a (fictitious) deformable body, but we assume, moreover, that the time coordinate is fixed. This is necessary for quantum mechanics, because the Hamiltonian operator depends on the choice of the time coordinate. Our definition allows us to associate rigorously with each reference frame F, a unique "space" (a three-dimensional differentiable manifold), which is the set of the world lines bound to F. This also is very useful for quantum mechanics. We briefly discuss the application of these concepts to G枚del's universe. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.3521v2-abstract-full').style.display = 'none'; document.getElementById('1003.3521v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 April, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages in standard 12pt format. v2: Discussion Section 4 reinforced, now includes an application to G枚del's universe.</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Int. J. Geometric Methods in Modern Physics Vol. 8, No. 1 (2011) 155-165 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1001.0460">arXiv:1001.0460</a> <span> [<a href="https://arxiv.org/pdf/1001.0460">pdf</a>, <a href="https://arxiv.org/ps/1001.0460">ps</a>, <a href="https://arxiv.org/format/1001.0460">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1742-6596/222/1/012042">10.1088/1742-6596/222/1/012042 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Non-uniqueness of the Dirac theory in a curved spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1001.0460v1-abstract-short" style="display: inline;"> We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. In this paper, we focus o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1001.0460v1-abstract-full').style.display = 'inline'; document.getElementById('1001.0460v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1001.0460v1-abstract-full" style="display: none;"> We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. In this paper, we focus on the standard version of the gravitational Dirac equation, but the non-uniqueness applies also to our alternative versions. We find that the changes which lead to an equivalent operator H, or respectively to an equivalent operator E, are determined by initial data, or respectively have to make some point-dependent antihermitian matrix vanish. Thus, the vast majority of the possible coefficient changes lead neither to an equivalent operator H, nor to an equivalent operator E, whence a lack of uniqueness. We show that even the Dirac energy spectrum is not unique. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1001.0460v1-abstract-full').style.display = 'none'; document.getElementById('1001.0460v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 January, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages (standard 12pt article format). Text of a talk given at the 1st Mediterranean Conference on Classical and Quantum Gravity, Kolymbari (Greece), Sept. 14-18, 2009</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Phys.Conf.Ser. 222:012042,2010 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0905.3686">arXiv:0905.3686</a> <span> [<a href="https://arxiv.org/pdf/0905.3686">pdf</a>, <a href="https://arxiv.org/ps/0905.3686">ps</a>, <a href="https://arxiv.org/format/0905.3686">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1002/andp.201100060">10.1002/andp.201100060 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A non-uniqueness problem of the Dirac theory in a curved spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0905.3686v4-abstract-short" style="display: inline;"> The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. We do that for the standard version of the gravitational Dirac equation, and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0905.3686v4-abstract-full').style.display = 'inline'; document.getElementById('0905.3686v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0905.3686v4-abstract-full" style="display: none;"> The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. We do that for the standard version of the gravitational Dirac equation, and for two alternative equations based on the tensor representation of the Dirac fields. The latter equations may be defined when the spacetime is four-dimensional, noncompact, and admits a spinor structure. We find that, for each among the three versions of the equation, the vast majority of the possible coefficient changes do not lead to an equivalent operator H, nor to an equivalent operator E, whence a lack of uniqueness. In particular, we prove that the Dirac energy spectrum is not unique. This non-uniqueness of the energy spectrum comes from an effect of the choice of coefficients, and applies in any given coordinates. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0905.3686v4-abstract-full').style.display = 'none'; document.getElementById('0905.3686v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 May, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 May, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 pages (standard article format). v4: Version accepted for publication in Annalen der Physik: Redactional improvements and precisions added in Section 2. Footnote added in the Conclusion, with new references. v3: Introduction and Conclusion reinforced. References added. v2: subsection 2.3 added: the Lagrangian and the spin group. Also, added explanations on admissible coefficient changes</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Annalen Phys.523:531-551,2011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0810.0671">arXiv:0810.0671</a> <span> [<a href="https://arxiv.org/pdf/0810.0671">pdf</a>, <a href="https://arxiv.org/ps/0810.0671">ps</a>, <a href="https://arxiv.org/format/0810.0671">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Quantum mechanics for three versions of the Dirac equation in a curved spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0810.0671v1-abstract-short" style="display: inline;"> We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The latter considers the Dirac wave function as a spacetime vector and the set of the Dirac matrices as a third-order tensor. Having the probability current cons… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0810.0671v1-abstract-full').style.display = 'inline'; document.getElementById('0810.0671v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0810.0671v1-abstract-full" style="display: none;"> We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The latter considers the Dirac wave function as a spacetime vector and the set of the Dirac matrices as a third-order tensor. Having the probability current conserved for any solution of the Dirac equation gives an equation to be satisfied by the coefficient fields. A positive definite scalar product is defined and a hermiticity condition for the Dirac Hamiltonian is derived for a general coordinate system in a general curved spacetime. For the standard equation, the hermiticity of the Dirac Hamiltonian is not preserved under all admissible changes of the coefficient fields. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0810.0671v1-abstract-full').style.display = 'none'; document.getElementById('0810.0671v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 October, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages in standard LaTeX. Text of a talk given at the 11th Conf. "Physical Interpretations of Relativity Theory", London, 12-15 Sept. 2008</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0807.0570">arXiv:0807.0570</a> <span> [<a href="https://arxiv.org/pdf/0807.0570">pdf</a>, <a href="https://arxiv.org/ps/0807.0570">ps</a>, <a href="https://arxiv.org/format/0807.0570">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1590/S0103-97332010000200020">10.1590/S0103-97332010000200020 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Basic quantum mechanics for three Dirac equations in a curved spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0807.0570v3-abstract-short" style="display: inline;"> We study the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime by extending Pauli's method. We further extend this study to three versions of the Dirac equation: the standard (Dirac-Fock-Weyl or DFW) equation, and two alternative versions, both of which are based on the recently proposed linear tensor representations of the Dirac field (TRD). We begin with… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0807.0570v3-abstract-full').style.display = 'inline'; document.getElementById('0807.0570v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0807.0570v3-abstract-full" style="display: none;"> We study the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime by extending Pauli's method. We further extend this study to three versions of the Dirac equation: the standard (Dirac-Fock-Weyl or DFW) equation, and two alternative versions, both of which are based on the recently proposed linear tensor representations of the Dirac field (TRD). We begin with the current conservation: we show that the latter applies to any solution of the Dirac equation, iff the field of Dirac matrices $纬^渭$ satisfies a specific PDE. This equation is always satisfied for DFW with its restricted choice for the $纬^渭$ matrices. It similarly restricts the choice of the $纬^渭$ matrices for TRD. However, this restriction can be achieved. The frame dependence of a general Hamiltonian operator is studied. We show that in any given reference frame with minor restrictions on the spacetime metric, the axioms of quantum mechanics impose a unique form for the Hilbert space scalar product. Finally, the condition for the general Dirac Hamiltonian operator to be Hermitian is derived in a general curved spacetime. For DFW, the validity of this hermiticity condition depends on the choice of the $纬^渭$ matrices. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0807.0570v3-abstract-full').style.display = 'none'; document.getElementById('0807.0570v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 July, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 pages (standard 12pt format). v3: Introduction reinforced, a few wording improvements in the body, former appendix removed and made into a paper, arXiv:1003.3521. v2: a few additional informations, e.g. regarding the similarity transformations that are allowable</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Braz.J.Phys.40:242-255,2010 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0708.3204">arXiv:0708.3204</a> <span> [<a href="https://arxiv.org/pdf/0708.3204">pdf</a>, <a href="https://arxiv.org/ps/0708.3204">ps</a>, <a href="https://arxiv.org/format/0708.3204">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physleta.2007.11.020">10.1016/j.physleta.2007.11.020 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Main effects of the Earth's rotation on the stationary states of ultra-cold neutrons </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0708.3204v3-abstract-short" style="display: inline;"> The relativistic corrections in the Hamiltonian for a particle in a uniformly rotating frame are discussed. They are shown to be negligible in the case of ultra-cold neutrons (UCN) in the Earth's gravity. The effect, on the energy levels of UCN, of the main term due to the Earth's rotation, i.e. the angular-momentum term, is calculated. The energy shift is found proportional to the energy level… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0708.3204v3-abstract-full').style.display = 'inline'; document.getElementById('0708.3204v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0708.3204v3-abstract-full" style="display: none;"> The relativistic corrections in the Hamiltonian for a particle in a uniformly rotating frame are discussed. They are shown to be negligible in the case of ultra-cold neutrons (UCN) in the Earth's gravity. The effect, on the energy levels of UCN, of the main term due to the Earth's rotation, i.e. the angular-momentum term, is calculated. The energy shift is found proportional to the energy level itself. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0708.3204v3-abstract-full').style.display = 'none'; document.getElementById('0708.3204v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 November, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 August, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages in standard LaTeX. v3: Former sect. 2 (derivation of the non-relativistic Hamiltonian) suppressed, new refs., interpretation of the energy shift added, and new redactional improvements, to meet the editorial demands. To appear in Physics Letters A</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Lett. A 372 (2008) 2196-2200 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0707.1829">arXiv:0707.1829</a> <span> [<a href="https://arxiv.org/pdf/0707.1829">pdf</a>, <a href="https://arxiv.org/ps/0707.1829">ps</a>, <a href="https://arxiv.org/format/0707.1829">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1590/S0103-97332008000200007">10.1590/S0103-97332008000200007 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dirac equation: Representation independence and tensor transformation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a>, <a href="/search/gr-qc?searchtype=author&query=Reifler%2C+F">Frank Reifler</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0707.1829v3-abstract-short" style="display: inline;"> We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak conditions on the affine coordinates, the current, as well as the spectrum of the Dirac Hamiltonian, thus all of quantum mechanics, are independent of that set. T… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0707.1829v3-abstract-full').style.display = 'inline'; document.getElementById('0707.1829v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0707.1829v3-abstract-full" style="display: none;"> We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak conditions on the affine coordinates, the current, as well as the spectrum of the Dirac Hamiltonian, thus all of quantum mechanics, are independent of that set. These results allow us to show that the tensor Dirac theory, which transforms the wave function as a spacetime vector and the set of Dirac matrices as a third-order affine tensor, is physically equivalent to the genuine Dirac theory, based on the spinor transformation. The tensor Dirac equation extends immediately to general coordinate systems, thus to non-inertial (e.g. rotating) coordinate systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0707.1829v3-abstract-full').style.display = 'none'; document.getElementById('0707.1829v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 April, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 July, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, standard LaTeX. v3: matches version accepted in the Brazilian Journal of Physics: minor wording improvements, refs updated. v2: Intro and Conclusion improved (novelty more emphasized). Uniqueness and positive definiteness extended to any admissible affine coordinates. 10 new refs</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Braz.J.Phys.38:248-258,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0706.4413">arXiv:0706.4413</a> <span> [<a href="https://arxiv.org/pdf/0706.4413">pdf</a>, <a href="https://arxiv.org/ps/0706.4413">ps</a>, <a href="https://arxiv.org/format/0706.4413">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/9789812776174_0031">10.1142/9789812776174_0031 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum wave equations in curved space-time from wave mechanics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0706.4413v1-abstract-short" style="display: inline;"> Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence. </span> <span class="abstract-full has-text-grey-dark mathjax" id="0706.4413v1-abstract-full" style="display: none;"> Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0706.4413v1-abstract-full').style.display = 'none'; document.getElementById('0706.4413v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 June, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">3 pages in 12pt LaTeX. Text of a talk given at the conference "Symmetry and Perturbation Theory", 2-9 June 2007, Otranto (Italy). Submitted to the Proceedings (G. Gaeta and Raff. Vitolo, eds, World Scientific)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0702048">arXiv:gr-qc/0702048</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0702048">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0702048">ps</a>, <a href="https://arxiv.org/format/gr-qc/0702048">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s10701-008-9249-6">10.1007/s10701-008-9249-6 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dirac-type equations in a gravitational field, with vector wave function </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0702048v4-abstract-short" style="display: inline;"> An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rul… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0702048v4-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0702048v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0702048v4-abstract-full" style="display: none;"> An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct Klein-Gordon equations and two distinct Dirac-type equations in a general metric, depending on the connection used. Each of these two equations is generally-covariant, transforms the wave function as a four-vector, and differs from the Fock-Weyl gravitational Dirac equation (DFW equation). One obeys the equivalence principle in an often-accepted sense, whereas the DFW equation obeys that principle only in an extended sense. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0702048v4-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0702048v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 October, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 February, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 pages. Version accepted for publication in Foundations of Physics. Title changed. Introduction expanded: detailed discussion of i) the vector Dirac wave function and ii) the status of the equivalence principle, main section (Sect. 2) improved by introducing the specific connection earlier (see Theorem 1), and other improvements accounting for the referees' remarks</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Found.Phys.38:1020-1045,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0612036">arXiv:gr-qc/0612036</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0612036">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> A theory of gravity as a pressure force. II. Lorentz contraction and "relativistic" effects </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0612036v1-abstract-short" style="display: inline;"> In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a scalar field equation has thus been proposed for gravity, giving a new theory in the compressible case. Here the theory is reinterpreted so as to describe the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0612036v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0612036v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0612036v1-abstract-full" style="display: none;"> In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a scalar field equation has thus been proposed for gravity, giving a new theory in the compressible case. Here the theory is reinterpreted so as to describe the relativistic effects, by extending the Lorentz-Poincar茅 interpretation of special relativity which is first recalled. Gravitational space-contraction and time-dilatation are postulated, as a consequence of the principle of local equivalence between the effects of motion and gravitation. The space-time metric (expressing the proper time along a trajectory) is hence curved also in the proposed theory. As the result of a modified Newton law, it is proved that free test particles follow geodesic lines of this metric. In the spherical static situation, Schwarzschild's exterior metric is exactly recovered and with it the experimental support of general relativity, but the interior solution as well as the problematic of singularities are different in the proposed theory, e.g. the radius of the body cannot be smaller than the Schwarzschild radius. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0612036v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0612036v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 December, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">21 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Rev.Roum.Sci.Tech.Ser.Mec.Appl. 38 (1993) 107-128 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0609051">arXiv:gr-qc/0609051</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0609051">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> On the extension of Newton's second law to theories of gravitation in curved space-time </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0609051v1-abstract-short" style="display: inline;"> We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric. This framework is first recalled, underlining the possibility to uniquely define a space metric and a local time in any given reference frame, hence to define v… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0609051v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0609051v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0609051v1-abstract-full" style="display: none;"> We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric. This framework is first recalled, underlining the possibility to uniquely define a space metric and a local time in any given reference frame, hence to define velocity and momentum in terms of the local space and time standards. It is shown that a unique consistent definition can be given for the derivative of a vector (the momentum) along a trajectory. Then the possible form of the gravitation force is investigated. It is shown that, if the motion of free particles has to follow space-time geodesics, then the expression for the gravity acceleration is determined uniquely. It depends on the variation of the metric with space and time, and it involves the velocity of the particle. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0609051v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0609051v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 September, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">32 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Arch.Mech. 48 (1996) 551-576 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0606036">arXiv:gr-qc/0606036</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0606036">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0606036">ps</a>, <a href="https://arxiv.org/format/gr-qc/0606036">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.74.065017">10.1103/PhysRevD.74.065017 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Post-Newtonian equation for the energy levels of a Dirac particle in a static metric </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0606036v2-abstract-short" style="display: inline;"> We study first the Hamiltonian operator H corresponding to the Fock-Weyl extension of the Dirac equation to gravitation. When searching for stationary solutions to this equation, in a static metric, we show that just one invariant Hermitian product appears natural. In the case of a space-isotropic metric, H is Hermitian for that product. Then we investigate the asymptotic post-Newtonian approxim… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0606036v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0606036v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0606036v2-abstract-full" style="display: none;"> We study first the Hamiltonian operator H corresponding to the Fock-Weyl extension of the Dirac equation to gravitation. When searching for stationary solutions to this equation, in a static metric, we show that just one invariant Hermitian product appears natural. In the case of a space-isotropic metric, H is Hermitian for that product. Then we investigate the asymptotic post-Newtonian approximation of the stationary Schroedinger equation associated with H, for a slow particle in a weak-field static metric. We rewrite the expanded equations as one equation for a two-component spinor field. This equation contains just the non-relativistic Schroedinger equation in the gravity potential, plus correction terms. Those "correction" terms are of the same order in the small parameter as the "main" terms, but are numerically negligible in the case of ultra-cold neutrons in the Earth's gravity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0606036v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0606036v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 September, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 June, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12pt LaTeX, 17 pages. v2: version accepted for publication in Phys.Rev.D: comments on scalar product changed, using a recent paper; discussion of PN expansions simplified (no change of units any more); numerical estimates for ultra-cold neutrons in the Earth's gravity</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D74 (2006) 065017 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0512046">arXiv:gr-qc/0512046</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0512046">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0512046">ps</a>, <a href="https://arxiv.org/format/gr-qc/0512046">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s10702-006-0514-7">10.1007/s10702-006-0514-7 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dirac equation from the Hamiltonian and the case with a gravitational field </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0512046v2-abstract-short" style="display: inline;"> Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies in the same form to a free particle, to one in an electromagnetic field, and to one subjected to geodesic motion in a static metric, and leads to the same, us… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0512046v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0512046v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0512046v2-abstract-full" style="display: none;"> Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies in the same form to a free particle, to one in an electromagnetic field, and to one subjected to geodesic motion in a static metric, and leads to the same, usual form of the Dirac equation--in special coordinates. To use the equation in the static-gravitational case, we need to rewrite it in more general coordinates. This can be done only if the usual, spinor transformation of the wave function is replaced by the 4-vector transformation. We show that the latter also makes the flat-space-time Dirac equation Lorentz-covariant, although the Dirac matrices are not invariant. Because the equation itself is left unchanged in the flat case, the 4-vector transformation does not alter the main physical consequences of that equation in that case. However, the equation derived in the static-gravitational case is not equivalent to the standard (Fock-Weyl) gravitational extension of the Dirac equation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0512046v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0512046v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 January, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 December, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">27 pages, standard LaTeX. v2: minor style changes, accepted for publication in Found. Phys. Letters</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Found.Phys.Lett.19:225-247,2006 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0510026">arXiv:gr-qc/0510026</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0510026">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0510026">ps</a>, <a href="https://arxiv.org/format/gr-qc/0510026">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> </div> <p class="title is-5 mathjax"> Equations of motion according to the asymptotic post-Newtonian scheme for general relativity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0510026v1-abstract-short" style="display: inline;"> We summarize a recent work done on the title's subject. First, we present the asymptotic scheme of post-Newtonian (PN) approximation for general relativity in the harmonic gauge. Then, we discuss the definition of the mass centers and the derivation of equations for their motion, following that scheme. Finally, we briefly analyze the reason why a new term has thus been found in the equations of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0510026v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0510026v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0510026v1-abstract-full" style="display: none;"> We summarize a recent work done on the title's subject. First, we present the asymptotic scheme of post-Newtonian (PN) approximation for general relativity in the harmonic gauge. Then, we discuss the definition of the mass centers and the derivation of equations for their motion, following that scheme. Finally, we briefly analyze the reason why a new term has thus been found in the equations of motion. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0510026v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0510026v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 October, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, no figure. Text of talks given at the 3rd Workshop "Gravity, Astrophysics and Strings at the Black Sea" (Kiten, Bulgaria, June 13-20, 2005). Submitted to the Proceedings (P. Fiziev and M. Todorov, eds.)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Gravity, Astrophysics and Strings at the Black Sea (P. Fiziev & M. Todorov, eds.), St. Kliment Ohridski University Press, Sofia (2006), pp. 1-9 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0504016">arXiv:gr-qc/0504016</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0504016">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0504016">ps</a>, <a href="https://arxiv.org/format/gr-qc/0504016">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.72.084002">10.1103/PhysRevD.72.084002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Equations of motion according to the asymptotic post-Newtonian scheme for general relativity in the harmonic gauge </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0504016v2-abstract-short" style="display: inline;"> The asymptotic scheme of post-Newtonian approximation defined for general relativity (GR) in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg's (1972) expansion of the metric and his general expansion of the energy-mom… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0504016v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0504016v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0504016v2-abstract-full" style="display: none;"> The asymptotic scheme of post-Newtonian approximation defined for general relativity (GR) in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg's (1972) expansion of the metric and his general expansion of the energy-momentum tensor ${\bf T}$, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of ${\bf T}$ for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in GR. To put them into a tractable form, we use an asymptotic framework for the separation parameter $畏$, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order $畏^3$ included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasi-spherical, in the sense that in all bodies the inertia tensor comes close to being spherical as $畏\to 0$. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0504016v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0504016v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 September, 2005; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 April, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">42 pages, no figure. Version accepted for publication in Physical Review D</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D72 (2005) 084002 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0412085">arXiv:gr-qc/0412085</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0412085">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0412085">ps</a>, <a href="https://arxiv.org/format/gr-qc/0412085">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1590/S0103-97332006000200010">10.1590/S0103-97332006000200010 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Space isotropy and weak equivalence principle in a scalar theory of gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0412085v3-abstract-short" style="display: inline;"> We consider a preferred-frame bimetric theory in which the scalar gravitational field both influences the metric and has direct dynamical effects. A modified version ("v2") is built, by assuming now a locally-isotropic dilation of physically measured distances, as compared with distances evaluated with the Euclidean space metric. The dynamical equations stay unchanged: they are based on a consis… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0412085v3-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0412085v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0412085v3-abstract-full" style="display: none;"> We consider a preferred-frame bimetric theory in which the scalar gravitational field both influences the metric and has direct dynamical effects. A modified version ("v2") is built, by assuming now a locally-isotropic dilation of physically measured distances, as compared with distances evaluated with the Euclidean space metric. The dynamical equations stay unchanged: they are based on a consistent formulation of Newton's second law in a curved space-time. To obtain a local conservation equation for energy with the new metric, the equation for the scalar field is modified: now its l.h.s. is the flat wave operator. Fluid dynamics is formulated and the asymptotic scheme of post-Newtonian approximation is adapted to v2. The latter also explains the gravitational effects on light rays, as did the former version (v1). The violation of the weak equivalence principle found for gravitationally-active bodies at the point-particle limit, which discarded v1, is proved to not exist in v2. Thus that violation was indeed due to the anisotropy of the space metric assumed in v1. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0412085v3-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0412085v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 January, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 December, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages. v3: Redactional improvements, e.g. on the balance equation for spatial momentum and on matter production, footnote added in conclusion on rotation effects. Accepted for publication in the Brazil. J. Phys.. v2: Introduction modified, a few wording improvements in the conclusion, references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Braz.J.Phys.36:177-189,2006 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0409092">arXiv:gr-qc/0409092</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0409092">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0409092">ps</a>, <a href="https://arxiv.org/format/gr-qc/0409092">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Scalar gravity with preferred frame: asymptotic post-Newtonian scheme and the weak equivalence principle </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0409092v1-abstract-short" style="display: inline;"> A scalar theory of gravity with a preferred reference frame is presented. It is insisted on the dynamics, which involves a (non-trivial) extension of Newton's second law, and on the new version (v2) with isotropic space metric. We display the energy conservation equation obtained with v2. Then the principles of the asymptotic post-Newtonian approximation are discussed in some detail. The results… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0409092v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0409092v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0409092v1-abstract-full" style="display: none;"> A scalar theory of gravity with a preferred reference frame is presented. It is insisted on the dynamics, which involves a (non-trivial) extension of Newton's second law, and on the new version (v2) with isotropic space metric. We display the energy conservation equation obtained with v2. Then the principles of the asymptotic post-Newtonian approximation are discussed in some detail. The results of its application to the motion of a small extended body in a weakly-gravitating system are given and discussed: the weak equivalence principle was violated in v1, due to its anisotropic space metric (as the standard Schwarzschild metric), but is valid with v2. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0409092v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0409092v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 September, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages (in the format here), text of talk given at the 2nd Workshop "Gravity, Astrophysics and Strings at the Black Sea" (Kiten, Bulgaria, June 10-16, 2004). Submitted to the Proceedings (P. Fiziev, R. Rashkov, and M. Todorov, eds.)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Gravity, Astrophysics and Strings at the Black Sea (P. P. Fiziev and M. D. Todorov, eds.), St. Kliment Ohridski University Press, Sofia (2005), pp. 1-16 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0401021">arXiv:gr-qc/0401021</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0401021">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0401021">ps</a>, <a href="https://arxiv.org/format/gr-qc/0401021">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Ether theory of gravitation: why and how? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0401021v2-abstract-short" style="display: inline;"> Gravitation might make a preferred frame appear, and with it a clear space/time separation--the latter being, a priori, needed by quantum mechanics (QM) in curved space-time. Several models of gravitation with an ether are discussed: they assume metrical effects in an heterogeneous ether and/or a Lorentz-symmetry breaking. One scalar model, starting from a semi-heuristic view of gravity as a pre… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0401021v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0401021v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0401021v2-abstract-full" style="display: none;"> Gravitation might make a preferred frame appear, and with it a clear space/time separation--the latter being, a priori, needed by quantum mechanics (QM) in curved space-time. Several models of gravitation with an ether are discussed: they assume metrical effects in an heterogeneous ether and/or a Lorentz-symmetry breaking. One scalar model, starting from a semi-heuristic view of gravity as a pressure force, is detailed. It has been developed to a complete theory including continuum dynamics, cosmology, and links with electromagnetism and QM. To test the theory, an asymptotic scheme of post-Newtonian approximation has been built. That version of the theory which is discussed here predicts an internal-structure effect, even at the point-particle limit. The same might happen also in general relativity (GR) in some gauges, if one would use a similar scheme. Adjusting the equations of planetary motion on an ephemeris leaves a residual difference with it; one should adjust the equations using primary observations. The same effects on light rays are predicted as with GR, and a similar energy loss applies to binary pulsars. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0401021v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0401021v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 May, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 January, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Standard LaTeX, 60 pages. Invited contribution to the book ``Ether, Spacetime and Cosmology" (M. C. Duffy, ed.), to appear at Hadronic Press. v2: minor improvements, new refs., post-scriptum summarizing later work</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Ether, space-time and cosmology, Vol. 1: Modern ether concepts, relativity and geometry (M. C. Duffy and J. Levy, Eds.), PD Publications, Liverpool, UK (2008), pp. 139-201. ISBN: 1 873 694 10 5 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0310062">arXiv:gr-qc/0310062</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0310062">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0310062">ps</a>, <a href="https://arxiv.org/format/gr-qc/0310062">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1023/B:TAMP.0000033037.42732.c5">10.1023/B:TAMP.0000033037.42732.c5 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Gravitational effects on light rays and binary pulsar energy loss in a scalar theory of gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0310062v1-abstract-short" style="display: inline;"> A scalar bimetric theory of gravity with a preferred reference frame is summarized. Dynamics is governed by an extension of Newton's second law. In the static case, geodesic motion is recovered together with Newton's attraction field. In the static spherical case, Schwarzschild's metric is found. Asymptotic schemes of post-Newtonian (PN) and post-Minkowskian (PM) approximation are built, each ba… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0310062v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0310062v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0310062v1-abstract-full" style="display: none;"> A scalar bimetric theory of gravity with a preferred reference frame is summarized. Dynamics is governed by an extension of Newton's second law. In the static case, geodesic motion is recovered together with Newton's attraction field. In the static spherical case, Schwarzschild's metric is found. Asymptotic schemes of post-Newtonian (PN) and post-Minkowskian (PM) approximation are built, each based on associating a conceptual family of systems with the given system. At the 1PN approximation, there is no preferred-frame effect for photons, hence the standard predictions of GR for photons are got. At the 0PM approximation, an isolated system loses energy by quadrupole radiation, without any monopole or dipole term. Inserting this loss into the Newtonian 2-body problem gives the Peters-Mathews coefficients of the theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0310062v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0310062v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 October, 2003; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2003. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">LaTeX, 26 pages, no figure. Accepted for publication in Theor. Math. Phys. (Teor. Mat. Fiz.)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Theor.Math.Phys. 140 (2004) 1011-1027; Teor.Mat.Fiz. 140 (2004) 139-159 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0309032">arXiv:gr-qc/0309032</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0309032">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0309032">ps</a>, <a href="https://arxiv.org/format/gr-qc/0309032">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Gravitational Energy Loss and Binary Pulsars in the Scalar Ether-Theory of Gravitation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0309032v1-abstract-short" style="display: inline;"> Motivation is given for trying a theory of gravity with a preferred reference frame (``ether'' for short). One such theory is summarized, that is a scalar bimetric theory. Dynamics is governed by an extension of Newton's second law. In the static case, geodesic motion is recovered together with Newton's attraction field. In the static spherical case, Schwarzschild's metric is got. An asymptotic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0309032v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0309032v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0309032v1-abstract-full" style="display: none;"> Motivation is given for trying a theory of gravity with a preferred reference frame (``ether'' for short). One such theory is summarized, that is a scalar bimetric theory. Dynamics is governed by an extension of Newton's second law. In the static case, geodesic motion is recovered together with Newton's attraction field. In the static spherical case, Schwarzschild's metric is got. An asymptotic scheme of post-Minkowskian (PM) approximation is built by associating a conceptual family of systems with the given weakly-gravitating system. It is more general than the post-Newtonian scheme in that the velocity may be comparable with $c$. This allows to justify why the 0PM approximation of the energy rate may be equated to the rate of the Newtonian energy, as is usually done. At the 0PM approximation of this theory, an isolated system loses energy by quadrupole radiation, without any monopole or dipole term. It seems plausible that the observations on binary pulsars (the pulse data) could be nicely fitted with a timing model based on this theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0309032v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0309032v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 September, 2003; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2003. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Text of a talk given at the 4th Conf. on Physics Beyond the Standard Model, Tegernsee, June 2003, submitted to the Proceedings (H. V. Klapdor-Kleingrothaus, ed.)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Beyond the Desert 2003, Proc. 4th Conf. on Particle Physics Beyond the Standard Model (H. V. Klapdor-Kleingrothaus, ed.), Springer Proceedings in Physics, vol. 92 (2004), pp. 471-483 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0306025">arXiv:gr-qc/0306025</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0306025">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0306025">ps</a>, <a href="https://arxiv.org/format/gr-qc/0306025">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Point-particle limit in a scalar theory of gravitation and the weak equivalence principle </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0306025v1-abstract-short" style="display: inline;"> A scalar theory with a preferred reference frame is summarized. To test that theory in celestial mechanics, an "asymptotic" post-Newtonian (PN) scheme has been developed. This associates a conceptual family of self-gravitating systems with the given system, in order to have a true small parameter available. The resulting equations for a weakly-self-gravitating system of extended bodies include i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0306025v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0306025v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0306025v1-abstract-full" style="display: none;"> A scalar theory with a preferred reference frame is summarized. To test that theory in celestial mechanics, an "asymptotic" post-Newtonian (PN) scheme has been developed. This associates a conceptual family of self-gravitating systems with the given system, in order to have a true small parameter available. The resulting equations for a weakly-self-gravitating system of extended bodies include internal-structure effects. The internal-structure influence subsists at the point-particle limit--a violation of the weak equivalence principle. If one could develop an "asymptotic" approximation scheme in general relativity also, this could plausibly be found there also, in a gauge where the PN space metric would not be "conformally Euclidean". <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0306025v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0306025v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 June, 2003; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2003. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">LaTeX, 6 pages. Text of a talk given at the Rencontres de Moriond: Gravitational Waves and Experimental Gravity, Les Arcs, France (March 22-29, 2003). Submitted to the Proceedings (J. Dumarchez, ed.)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Gravitational waves and experimental gravity, Proc. of the 38th Rencontres de Moriond (J. Dumarchez & J. Tran Thanh Van, eds.), The Gioi, Hanoi (2004), pp. 377-382 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0305078">arXiv:gr-qc/0305078</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0305078">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0305078">ps</a>, <a href="https://arxiv.org/format/gr-qc/0305078">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> </div> <p class="title is-5 mathjax"> Testing a theory of gravity in celestial mechanics: a new method and its first results for a scalar theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0305078v2-abstract-short" style="display: inline;"> A new method of post-Newtonian approximation (PNA) for weak gravitational fields is presented together with its application to test an alternative, scalar theory of gravitation. The new method consists in defining a one-parameter family of systems, by applying a Newtonian similarity transformation to the initial data that defines the system of interest. This method is rigorous. Its difference wi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0305078v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0305078v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0305078v2-abstract-full" style="display: none;"> A new method of post-Newtonian approximation (PNA) for weak gravitational fields is presented together with its application to test an alternative, scalar theory of gravitation. The new method consists in defining a one-parameter family of systems, by applying a Newtonian similarity transformation to the initial data that defines the system of interest. This method is rigorous. Its difference with the standard PNA is emphasized. In particular, the new method predicts that the internal structure of the bodies does have an influence on the motion of the mass centers. The translational equations of motion obtained with this method in the scalar theory are adjusted in the solar system, and compared with an ephemeris based on the standard PNA of GR. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0305078v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0305078v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 June, 2003; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 May, 2003; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2003. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2: links to quoted arXiv papers. LaTeX, 28 pages including 2 figures. This is a revised version of a lecture given at the 8th. Conf. ``Physical Interpretations of Relativity Theory'' (London, September 2002), organized by the British Society for the Philosophy of Sciences. The initial version will appear in the proceedings of that conference (M. C. Duffy, ed.)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> RecentRes.Dev.Astron.Astrophys.1:859-879,2003 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0301031">arXiv:gr-qc/0301031</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0301031">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> </div> <p class="title is-5 mathjax"> Motion of the mass centers in a scalar theory of gravitation: the point particle limit </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0301031v3-abstract-short" style="display: inline;"> We investigate the point-particle limit of the equations of motion valid for a system of extended bodies in a scalar alternative theory of gravitation: the size of one of the bodies being a small parameter xi, we calculate the limit, as xi tends towards 0, of the post-Newtonian (PN) acceleration of this small body. We use the asymptotic scheme of PN approximation, that expands all fields. We fin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0301031v3-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0301031v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0301031v3-abstract-full" style="display: none;"> We investigate the point-particle limit of the equations of motion valid for a system of extended bodies in a scalar alternative theory of gravitation: the size of one of the bodies being a small parameter xi, we calculate the limit, as xi tends towards 0, of the post-Newtonian (PN) acceleration of this small body. We use the asymptotic scheme of PN approximation, that expands all fields. We find that the PN acceleration A of the small body keeps a structure-dependent part at this limit. In particular, if the only massive body is static and spherical, then A differs from the PN acceleration of a test particle in a Schwarzschild field only by this structure-dependent part. The presence of the latter is due to the fact that the PN metric depends on the first spatial derivatives of the Newtonian potential. Since just the same form of PN metric is valid for the standard form of Schwarzschild's solution, the acceleration of a small body might keep a structure-dependent part at the point limit in general relativity also, depending on the gauge. The magnitude of the structure-dependent acceleration is already challenging on Earth. For the Pioneer spacecrafts, it is likely to discard the current version of the scalar theory. A modified version has been outlined in a quoted reference. Keywords: Weak equivalence principle violation, Asymptotic post-Newtonian scheme <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0301031v3-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0301031v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 August, 2004; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 January, 2003; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2003. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">PDF, 22 pages. v3: Magnitude of the WEP violation for the Pioneer spacecrafts estimated more precisely (Sect. 6). Result: anisotropic-metric version of the scalar theory discarded (Conclusion). Former Sect. 2 suppressed, new references added. v2: minor corrections on pp. 10, 12 and 14</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Romanian Journal of Physics, Volume 49, Numbers 7-8, 2004, pp. 549 - 572 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0205105">arXiv:gr-qc/0205105</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0205105">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0205105">ps</a>, <a href="https://arxiv.org/format/gr-qc/0205105">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0217751X0201323X">10.1142/S0217751X0201323X <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Scalar Ether-Theory of Gravitation and its First Test in Celestial Mechanics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0205105v1-abstract-short" style="display: inline;"> The motivations for investigating a theory of gravitation based on a concept of "ether" are discussed-- a crucial point is the existence of an alternative interpretation of special relativity, named the Lorentz-Poincar茅 ether theory. The basic equations of one such theory of gravity, based on just one scalar field, are presented. To check this theory in celestial mechanics, an "asymptotic" schem… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0205105v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0205105v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0205105v1-abstract-full" style="display: none;"> The motivations for investigating a theory of gravitation based on a concept of "ether" are discussed-- a crucial point is the existence of an alternative interpretation of special relativity, named the Lorentz-Poincar茅 ether theory. The basic equations of one such theory of gravity, based on just one scalar field, are presented. To check this theory in celestial mechanics, an "asymptotic" scheme of post-Newtonian (PN) approximation is summarized and its difference with the standard PN scheme is emphasized. The derivation of PN equations of motion for the mass centers, based on the asymptotic scheme, is outlined. They are implemented for the major bodies of the solar system and the prediction for Mercury is compared with an ephemeris based on general relativity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0205105v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0205105v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 May, 2002; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2002. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">LaTeX, 6 pages, one figure. Text of a talk at the 5th Friedmann International Seminar on Gravitation and Cosmology, Joao Pessoa (Brazil), 23-30 April 2002. Will be submitted to a special issue of Int. J. Mod. Phys./A</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Int.J.Mod.Phys. A17 (2002) 4203-4208 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0203104">arXiv:gr-qc/0203104</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0203104">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0203104">ps</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Remarks on the mathematical origin of wave mechanics and consequences for a quantum mechanics in a gravitational field </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0203104v1-abstract-short" style="display: inline;"> According to Schroedinger's ideas, classical dynamics of point particles should correspond to the " geometrical optics " limit of a linear wave equation, in the same way as ray optics is the limit of wave optics. It is shown that, using notions of modern wave theory, the " geometrical optics " analogy leads to the correspondence between a classical Hamiltonian H and a " quantum " wave equation i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0203104v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0203104v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0203104v1-abstract-full" style="display: none;"> According to Schroedinger's ideas, classical dynamics of point particles should correspond to the " geometrical optics " limit of a linear wave equation, in the same way as ray optics is the limit of wave optics. It is shown that, using notions of modern wave theory, the " geometrical optics " analogy leads to the correspondence between a classical Hamiltonian H and a " quantum " wave equation in a natural and general way. In particular, the correspondence is unambiguous also in the case where H contains mixed terms involving momentum and position. In the line of Schroedinger's ideas, it is also attempted to justify the occurrence, in QM, of eigenvalues problems, not merely for energy, but also for momentum. It is shown that the wave functions of pure momentum states can be defined in a physically more satisfying way than by assuming plane waves. In the case of a spatially uniform force field, such momentum states have a singularity and move undeformed according to Newton's second law. The mentioned unambiguous correspondence allows to uniquely extend the Klein-Gordon relativistic wave equation to the case where a constant gravitational field is present. It is argued that Schroedinger's wave mechanics can be extended to the case with a variable gravitational field only if one accepts that the wave equation is a preferred-frame one. From this viewpoint, generally-covariant extensions of the wave equations of QM seem rather formal. Finally, it is conjectured that there is no need for a quantum gravity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0203104v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0203104v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 March, 2002; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2002. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">PS, 23 pages. Sixth International Conference "Physical Interpretations of Relativity Theory" (London, September 1998), Proceedings (M.C. Duffy, edr.), British Soc. Philos. Sci. /University of Sunderland, 1998, pp. 1-17. Font changed here</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Interpretations of Relativity Theory VI, Proceedings (M.C. Duffy, edr.), British Soc. Philos. Sci. /University of Sunderland (1998), pp. 1-17 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0202029">arXiv:gr-qc/0202029</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0202029">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> </div> <p class="title is-5 mathjax"> Equations of motion of the mass centers in a scalar theory of gravitation: Expansion in the separation parameter </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0202029v3-abstract-short" style="display: inline;"> An asymptotic framework is defined for the small parameter eta which quantifies a good separation between the extended bodies that make a weakly gravitating system. This is introduced within an alternative scalar theory of gravitation, though it may be defined similarly in other theories. This framework allows one to truncate the translational equations of motion at any well-defined order. Here,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0202029v3-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0202029v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0202029v3-abstract-full" style="display: none;"> An asymptotic framework is defined for the small parameter eta which quantifies a good separation between the extended bodies that make a weakly gravitating system. This is introduced within an alternative scalar theory of gravitation, though it may be defined similarly in other theories. This framework allows one to truncate the translational equations of motion at any well-defined order. Here, the post-Newtonian (PN) equations valid in the scalar theory are truncated beyond the order eta^3. The PN approximation scheme used is the asymptotic scheme, that expands all fields. To get the explicit form of the equations of motion for the mass centers, the bodies are assumed spherical, merely for calculating the PN corrections. It is found that, due to the use of the asymptotic PN scheme, the internal structure of the bodies does play a role in the equations of motion. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0202029v3-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0202029v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 August, 2003; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 February, 2002; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2002. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">PDF, 15 pages. v3: still a few redactional improvements, 4 references added, former Sect. 2 (previous results) removed, calculations relegated to an Appendix; accepted for publication in the Roman. J. Physics. v2: Some redactional improvements, and former Sect. 7 (point particle limit) removed. The reason for this is given on p. 8, after Eq. (4.6), in the new work gr-qc/0301031, which is entirely devoted to the point particle limit</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Roman. J. Phys., Vol. 48, Nos. 7-10, 805-820 (2003). </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/astro-ph/0112266">arXiv:astro-ph/0112266</a> <span> [<a href="https://arxiv.org/pdf/astro-ph/0112266">pdf</a>, <a href="https://arxiv.org/ps/astro-ph/0112266">ps</a>, <a href="https://arxiv.org/format/astro-ph/0112266">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1051/0004-6361:20011791">10.1051/0004-6361:20011791 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Proper initial conditions for long-term integrations of the solar system </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="astro-ph/0112266v2-abstract-short" style="display: inline;"> An optimization program is used to re-adjust the initial conditions, in order to reproduce as closely as possible the predictions of a complete ephemeris by using simplified equations of motion in the numerical integration. The adjustment of the initial conditions is illustrated in the transition from the DE406 complete long-range ephemeris to a Newtonian model considering only the Sun and the f… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('astro-ph/0112266v2-abstract-full').style.display = 'inline'; document.getElementById('astro-ph/0112266v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="astro-ph/0112266v2-abstract-full" style="display: none;"> An optimization program is used to re-adjust the initial conditions, in order to reproduce as closely as possible the predictions of a complete ephemeris by using simplified equations of motion in the numerical integration. The adjustment of the initial conditions is illustrated in the transition from the DE406 complete long-range ephemeris to a Newtonian model considering only the Sun and the four major planets. It is also used to best reproduce this same DE406 ephemeris, based on post-Newtonian equations for a system of mass points and including the Moon and asteroids, by using a Newtonian calculation corrected by the Schwarzschild effects of the Sun and restricted to the ten major bodies of the solar system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('astro-ph/0112266v2-abstract-full').style.display = 'none'; document.getElementById('astro-ph/0112266v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 January, 2002; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 December, 2001; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2001. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, accepted for publication in A&A. v2: TeX file instead of PS generated from word proc. as before</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Astron.Astrophys. 383 (2002) 729-737 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0106087">arXiv:gr-qc/0106087</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0106087">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0106087">ps</a>, <a href="https://arxiv.org/format/gr-qc/0106087">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> </div> <p class="title is-5 mathjax"> Comparison between two methods of post-Newtonian expansion for the motion in a weak Schwarzschild field </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0106087v3-abstract-short" style="display: inline;"> The asymptotic method of post-Newtonian (PN) expansion for weak gravitational fields, recently developed, is compared with the standard method of PN expansion, in the particular case of a massive test particle moving along a geodesic line of a weak Schwarzschild field. First, the expression of the active mass in Schwarzschild's solution is given for a barotropic perfect fluid, both for general r… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0106087v3-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0106087v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0106087v3-abstract-full" style="display: none;"> The asymptotic method of post-Newtonian (PN) expansion for weak gravitational fields, recently developed, is compared with the standard method of PN expansion, in the particular case of a massive test particle moving along a geodesic line of a weak Schwarzschild field. First, the expression of the active mass in Schwarzschild's solution is given for a barotropic perfect fluid, both for general relativity (GR) and for an alternative, scalar theory. The principle of the asymptotic method is then recalled and the PN expansion of the active mass is derived. The PN correction to the active mass is made of the Newtonian elastic energy, augmented, for the scalar theory, by a term due to the self-reinforcement of the gravitational field. Third, two equations, both correct to first order, are derived for the geodesic motion of a mass particle: a "standard" one and an "asymptotic" one. Finally, the difference between the solutions of these two equations is numerically investigated in the case of Mercury. The asymptotic solution deviates from the standard one like the square of the time elapsed since the initial time. This is due to a practical shortcoming of the asymptotic method, which is shown to disappear if one reinitializes the asymptotic problem often enough. Thus, both methods are equivalent in the case investigated. In a general case, the asymptotic method seems more natural. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0106087v3-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0106087v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 December, 2001; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 June, 2001; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2001. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">PostScript, 12 pages, 3 figures in 2 additional PS files. Accepted for publication in Nuovo Cimento B. V3: a few typos in V2, plus one sentence (p.10), corrected. V2: the cure outlined in V1, to remedy a numerical shortcoming of the asymptotic method, has been implemented. Result: in the investigated case of a test particle in a weak Schwarzschild field, the standard and asymptotic methods of PN expansion are definitely equivalent, also numerically</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nuovo Cim.B116:1277-1290,2001 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/astro-ph/0105217">arXiv:astro-ph/0105217</a> <span> [<a href="https://arxiv.org/pdf/astro-ph/0105217">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> A numerical solution of the inverse problem in classical celestial mechanics, with application to Mercury's motion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="astro-ph/0105217v2-abstract-short" style="display: inline;"> It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points is described and its high accuracy is verified. The osculating elements are also accurately computed. This solution is implemented in the Gauss iterative algor… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('astro-ph/0105217v2-abstract-full').style.display = 'inline'; document.getElementById('astro-ph/0105217v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="astro-ph/0105217v2-abstract-full" style="display: none;"> It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points is described and its high accuracy is verified. The osculating elements are also accurately computed. This solution is implemented in the Gauss iterative algorithm for solving nonlinear least-squares problems. This algorithm is summarized and its efficiency for the inverse problem in celestial mechanics is checked on a 3-bodies problem. Then it is used to assess the accuracy to which a Newtonian calculation may reproduce the DE403 ephemeris, that involves general-relativistic corrections. The parameter optimization allows to reduce the norm and angular differences between the Newtonian calculation and DE403 by a factor 10 (Mercury, Pluto) to 100 (Venus). The maximum angular difference on the heliocentric positions of Mercury is ca. 220" per century before the optimization, and ca. 20" after it. The latter is still far above the observational accuracy. On the other hand, Mercury's longitude of the perihelion is not affected by the optimization: it keeps the linear advance of 43" per century. Key words: Mercury's perihelion. Parameter optimization. Mechanics of point masses. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('astro-ph/0105217v2-abstract-full').style.display = 'none'; document.getElementById('astro-ph/0105217v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 November, 2002; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 May, 2001; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2001. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2: PDF, 17 pages including 4 figures, accepted for publication in Meccanica. Discussion improved, title changed, former Sects. 2-3 summarized to make the new Sect. 2, one figure more</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Meccanica 39 (2004) 17-29 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0103025">arXiv:gr-qc/0103025</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0103025">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0103025">ps</a>, <a href="https://arxiv.org/format/gr-qc/0103025">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/9789812777386_0169">10.1142/9789812777386_0169 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On a scalar theory of gravitation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0103025v1-abstract-short" style="display: inline;"> That preferred-frame theory accounts for special relativity and reduces to it if the gravitation field cancels. Starting from an interpretation of gravity as a pressure force, it is based on just one scalar field. This scalar gives the relation between the flat "background" metric and the curved "physical" metric, due to an equivalence principle between the absolute effects of motion and gravita… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0103025v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0103025v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0103025v1-abstract-full" style="display: none;"> That preferred-frame theory accounts for special relativity and reduces to it if the gravitation field cancels. Starting from an interpretation of gravity as a pressure force, it is based on just one scalar field. This scalar gives the relation between the flat "background" metric and the curved "physical" metric, due to an equivalence principle between the absolute effects of motion and gravitation. The scalar is also a potential for the gravity acceleration vector. Motion is governed by an extension of the special-relativistic form of Newton's second law. This provides a new equation for continuum dynamics, that gives the gravitational modification of Maxwell's equations, consistent with photon dynamics. The same effects on light rays as in GR are predicted at the post-Newtonian approximation (PNA). An asymptotic PNA is being studied, in order to build a consistent celestial mechanics in the theory. The cosmic acceleration is predicted and nonsingular cosmological models are obtained. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0103025v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0103025v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 March, 2001; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2001. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">TEX, 2 pages. Texte of a communication presented at the 9th Marcel Grossmann Meeting, Roma, July 2000. Submitted to the Proceedings of the Meeting</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/astro-ph/0006093">arXiv:astro-ph/0006093</a> <span> [<a href="https://arxiv.org/pdf/astro-ph/0006093">pdf</a>, <a href="https://arxiv.org/ps/astro-ph/0006093">ps</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Equations of motion for the mass centers in a scalar theory of gravitation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="astro-ph/0006093v1-abstract-short" style="display: inline;"> A scalar theory of gravitation with a preferred reference frame (PRF) is considered, that accounts for special relativity and reduces to it if the gravitational field cancels. The gravitating system consists of a finite number of perfect-fluid bodies. An " asymptotic " post-Newtonian (PN) approximation scheme is used, allowing an explicit weak-field limit with all fields expanded. Exact mass cen… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('astro-ph/0006093v1-abstract-full').style.display = 'inline'; document.getElementById('astro-ph/0006093v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="astro-ph/0006093v1-abstract-full" style="display: none;"> A scalar theory of gravitation with a preferred reference frame (PRF) is considered, that accounts for special relativity and reduces to it if the gravitational field cancels. The gravitating system consists of a finite number of perfect-fluid bodies. An " asymptotic " post-Newtonian (PN) approximation scheme is used, allowing an explicit weak-field limit with all fields expanded. Exact mass centers are defined and their exact equations of motion are derived. The PN expansion of these equations is obtained: the zero-order equations are those of Newtonian gravity (NG), and the equations for the first-order (PN) corrections depend linearly on the PN fields. For PN corrections to the motion of the mass centers, especially in the solar system, one may assume " very-well-separated " rigidly moving bodies with spherical self-fields of the zero-order approximation. The PN corrections reduce then to a time integration and include spin effects, which might be significant. It is shown that the Newtonian masses are not correct zero-order masses for the PN calculations. An algorithm is proposed, in order to minimize the residual and to assess the velocity in the PRF. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('astro-ph/0006093v1-abstract-full').style.display = 'none'; document.getElementById('astro-ph/0006093v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 June, 2000; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2000. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Post-Script, 32 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Rom.J.Phys. 45 (2000) 645-678 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0003066">arXiv:gr-qc/0003066</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0003066">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0003066">ps</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Asymptotic expansions for relativistic celestial mechanics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0003066v1-abstract-short" style="display: inline;"> The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory is summarized, then the relevant boundary problem is seen to be the full initial-value problem. It is shown that, with any given system of gravitating bodies,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0003066v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0003066v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0003066v1-abstract-full" style="display: none;"> The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory is summarized, then the relevant boundary problem is seen to be the full initial-value problem. It is shown that, with any given system of gravitating bodies, one may associate a one-parameter family of similar systems, the parameter measuring the gravitational field-strength. After a specific change of units, the derivation of asymptotic expansions becomes straightforward. Two hypotheses could be made as to which time variable has to be used in the expansion. The first one leads to an "asymptotic" post-Newtonian approximation (PNA) with instantaneous propagation, differing from the standard PNA in that, in the asymptotic PNA, all fields are expanded. The second hypothese could lead to an "asymptotic" post-Minkowskian approximation (PMA) allowing to describe propagation effects, but it is not compatible with the Newtonian limit. It is shown that the standard PNA is not compatible with the application of the usual method of asymptotic expansions as envisaged here. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0003066v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0003066v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 March, 2000; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2000. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">PS, 21 pages. To appear in the Romanian Journal of Physics</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Rom.J.Phys. 45 (2000) 389-414 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/9912070">arXiv:gr-qc/9912070</a> <span> <a href="https://arxiv.org/format/gr-qc/9912070">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Weak-field approximation of a scalar theory of gravitation and some remarks on the propagation effects of gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/9912070v3-abstract-short" style="display: inline;"> A simple example is given of the implementation of the usual method of asymptotic expansions for weak gravitational fields. A scalar, preferred-frame theory of gravitation is considered, but the method is general. Two kinds of asymptotic expansion are a priori possible: "post-Newtonian" (PN) or "post-Minkowskian", the latter allowing to account directly for propagation effects. However, it is sh… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9912070v3-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9912070v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9912070v3-abstract-full" style="display: none;"> A simple example is given of the implementation of the usual method of asymptotic expansions for weak gravitational fields. A scalar, preferred-frame theory of gravitation is considered, but the method is general. Two kinds of asymptotic expansion are a priori possible: "post-Newtonian" (PN) or "post-Minkowskian", the latter allowing to account directly for propagation effects. However, it is shown that only the PN asymptotic expansion is compatible with the Newtonian limit. It is also shown that, in the scalar theory, there is no non-Newtonian effect (in particular, no propagation effect) up to the second order, i.e., the order 1/c^2. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9912070v3-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9912070v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 January, 2000; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 December, 1999; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 1999. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, HTML. In the previous version, the author believed to have found a post-Minskowskian approximation which was consistent with both the usual method of asymptotic expansions and the Newtonian limit. It is now shown that only the post-Newtonian approximation with instantaneous propagation meets these two requirements, and the mistake that was done is pointed out. Method and main conclusion unchanged: no non-Newtonian effect before 1/c^2. One reference added</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/9912041">arXiv:gr-qc/9912041</a> <span> <a href="https://arxiv.org/format/gr-qc/9912041">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Post-Newtonian Approximation of a Scalar Theory of Gravitation and Application to Light Rays </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/9912041v1-abstract-short" style="display: inline;"> A scalar, preferred-frame theory of gravitation is summarized. Space-time is endowed with both a flat metric and a curved, "physical" metric. Motion is governed by a natural extension of Newton's second law, which implies geodesic motion only for a static field. The theory predicts Schwarzschild's exterior metric in the spherical static situation. It also predicts gravitation waves with the velo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9912041v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9912041v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9912041v1-abstract-full" style="display: none;"> A scalar, preferred-frame theory of gravitation is summarized. Space-time is endowed with both a flat metric and a curved, "physical" metric. Motion is governed by a natural extension of Newton's second law, which implies geodesic motion only for a static field. The theory predicts Schwarzschild's exterior metric in the spherical static situation. It also predicts gravitation waves with the velocity of light. The equations of motion are recast into the "flat space - uniform time" form, and compared with the geodesic equations of motion. The principles of the post-Newtonian approximation of this theory are given, including the way to account for preferred-frame effects. This approximation is then developed more particularly for photons. It is found that the preferred-frame effects do not occur in this case, nor does the difference between Newton's second law and geodesic assumption. Thus, the post-Newtonian predictions of this theory for photons are indistinguishable from the standard post-Newtonian predictions of general relativity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9912041v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9912041v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 December, 1999; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 1999. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">HTML, 17 pages, no figure.Accepted (Summer 1996) for publication in Rev. Roum. Sci. Tech. - Mec. Appl.. Apart from reference 22 (added) and note 2 (modified), this text dates back to May 1996</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Rev.Roum.Sci.Tech.Ser.Mec.Appl. 43 (1998) 135-153 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/9911057">arXiv:gr-qc/9911057</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/9911057">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/9911057">ps</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> </div> </div> <p class="title is-5 mathjax"> Accelerated Expansion as Predicted by an Ether Theory of Gravitation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Arminjon%2C+M">Mayeul Arminjon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/9911057v4-abstract-short" style="display: inline;"> Cosmology is investigated within a new, scalar theory of gravitation, which is a preferred-frame bimetric theory with flat background metric. Before coming to cosmology, the motivation for an " ether theory " is exposed at length; the investigated concept of ether is presented: it is a compressible fluid, and gravity is seen as Archimedes' thrust due to the pressure gradient in that fluid. The c… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9911057v4-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9911057v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9911057v4-abstract-full" style="display: none;"> Cosmology is investigated within a new, scalar theory of gravitation, which is a preferred-frame bimetric theory with flat background metric. Before coming to cosmology, the motivation for an " ether theory " is exposed at length; the investigated concept of ether is presented: it is a compressible fluid, and gravity is seen as Archimedes' thrust due to the pressure gradient in that fluid. The construction of the theory is explained and the current status of the experimental confrontation is analysed, both in some detail. An analytical cosmological solution is obtained for a general form of the energy-momentum tensor. According to that theory, expansion is necessarily accelerated, both by vacuum and even by matter. In one case, the theory predicts expansion, the density increasing without limit as time goes back to infinity. High density is thus obtained in the past, without a big-bang singularity. In the other case, the Universe follows a sequence of (non-identical) contraction-expansion cycles, each with finite maximum energy density; the current expansion phase will end by infinite dilution in some six billions of years. The density ratio of the present cycle (ratio of the maximum to current densities) is not determined by the current density and the current Hubble constant H0, unless a special assumption is made. Since cosmological redshifts approaching z = 4 are observed, the density ratio should be at least 100. From this and the estimate of H0, the time spent since the maximum density is constrained to be larger than several hundreds of billions of years. Yet if a high density ratio, compatible with the standard explanation for the light elements and the 2.7 K radiation, is assumed, then the age of the Universe is much larger still. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9911057v4-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9911057v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 June, 2001; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 November, 1999; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 1999. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">32 pages, Post-Script. v4 : Section 2 (general presentation of the theory and its motivation) still reinforced, Subsection 5.3 added (Comments on accelerated expansion and infinite dilution). To appear in "Physics Essays", Vol. 14, No. 1, 2001</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Essays 14 (2001) 10-32 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 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