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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/2406.01498">arXiv:2406.01498</a> <span> [<a href="https://arxiv.org/pdf/2406.01498">pdf</a>, <a href="https://arxiv.org/format/2406.01498">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/10.1088/1475-7516/2024/10/002">10.1088/1475-7516/2024/10/002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Ju%C3%A1rez-Aubry%2C+B+A">Benito A. Ju谩rez-Aubry</a>, <a href="/search/gr-qc?searchtype=author&query=Kay%2C+B+S">Bernard S. Kay</a>, <a href="/search/gr-qc?searchtype=author&query=Miramontes%2C+T">Tonatiuh Miramontes</a>, <a href="/search/gr-qc?searchtype=author&query=Sudarsky%2C+D">Daniel Sudarsky</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="2406.01498v3-abstract-short" style="display: inline;"> Given a Cauchy surface in a curved spacetime and a suitably defined quantum state on the CCR algebra of the Klein-Gordon quantum field on that surface, we show, by expanding the squared spacetime geodesic distance and the `$U$' and `$V$' Hadamard coefficients (and suitable derivatives thereof) in sufficiently accurate covariant Taylor expansions on the surface that the renormalized expectation val… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.01498v3-abstract-full').style.display = 'inline'; document.getElementById('2406.01498v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.01498v3-abstract-full" style="display: none;"> Given a Cauchy surface in a curved spacetime and a suitably defined quantum state on the CCR algebra of the Klein-Gordon quantum field on that surface, we show, by expanding the squared spacetime geodesic distance and the `$U$' and `$V$' Hadamard coefficients (and suitable derivatives thereof) in sufficiently accurate covariant Taylor expansions on the surface that the renormalized expectation value of the quantum stress-energy tensor on the surface is determined by the geometry of the surface and the first 4 time derivatives of the metric off the surface, in addition to the Cauchy data for the field's two-point function. This result has been anticipated in and is motivated by a previous investigation by the authors on the initial value problem in semiclassical gravity, for which the geometric initial data corresponds {\it a priori} to the metric on the surface and up to 3 time derivatives off the surface, but where it was argued that the fourth derivative can be obtained with aid of the field equations on the initial surface. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.01498v3-abstract-full').style.display = 'none'; document.getElementById('2406.01498v3-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> 22 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </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">65 pages, discussion improved</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JCAP 10 (2024) 002 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.11671">arXiv:2205.11671</a> <span> [<a href="https://arxiv.org/pdf/2205.11671">pdf</a>, <a href="https://arxiv.org/ps/2205.11671">ps</a>, <a href="https://arxiv.org/format/2205.11671">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/10.1088/1475-7516/2023/01/040">10.1088/1475-7516/2023/01/040 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the initial value problem for semiclassical gravity without and with quantum state collapses </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Ju%C3%A1rez-Aubry%2C+B+A">Benito A. Ju谩rez-Aubry</a>, <a href="/search/gr-qc?searchtype=author&query=Kay%2C+B+S">Bernard S. Kay</a>, <a href="/search/gr-qc?searchtype=author&query=Miramontes%2C+T">Tonatiuh Miramontes</a>, <a href="/search/gr-qc?searchtype=author&query=Sudarsky%2C+D">Daniel Sudarsky</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="2205.11671v5-abstract-short" style="display: inline;"> We explore how the initial value problem may be formulated for globally hyperbolic, Hadamard, solutions of the semiclassical Einstein-Klein-Gordon equations. Given a set of data on an initial 3-surface, consisting of the values on the surface of a spacetime metric and its first 3 time derivatives off the surface, we introduce a notion of 'surface Hadamard' state on the CCR algebra of the surface.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.11671v5-abstract-full').style.display = 'inline'; document.getElementById('2205.11671v5-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.11671v5-abstract-full" style="display: none;"> We explore how the initial value problem may be formulated for globally hyperbolic, Hadamard, solutions of the semiclassical Einstein-Klein-Gordon equations. Given a set of data on an initial 3-surface, consisting of the values on the surface of a spacetime metric and its first 3 time derivatives off the surface, we introduce a notion of 'surface Hadamard' state on the CCR algebra of the surface. We conjecture that, for a given such set of classical Cauchy data with a surface Hadamard state satisfying the semiclassical constraint equations, the initial value problem will be well posed. We present similar conjectures for a semiclassical scalars model and semiclassical electrodynamics. Moreover, partly inspired by work of Parker and Simon in 1993, we define semiclassical gravity `physical solutions' to be those that are (jointly smooth) functions of $\hbar$ and of coordinates continuous in $\hbar$ at $\hbar =0$. We conjecture that for such solutions the second and third time derivatives of the metric off the surface need not be specified, but rather will be determined by that continuity condition. Assuming the initial value conjecture for such physical solutions holds, and that a stochastic rule were available which leads to quantum state collapses occurring on (non-intersecting) random Cauchy surfaces, we discuss the well-posedness of semiclassical gravity with stochastic quantum state collapses. We also discuss two notions of approximate physical semiclassical solutions (both with and without collapses): Namely solutions to order $\hbar$ (first discussed by Parker and Simon in 1993) and solutions to order $\hbar^0$. We point out that the latter do not require higher derivative terms or Hadamard subtractions, but that nevertheless order $\hbar^0$ semiclassical gravity is a distinct theory from classical general relativity capable of incorporating quantum interference phenomena. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.11671v5-abstract-full').style.display = 'none'; document.getElementById('2205.11671v5-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 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </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">47 pages. Corrections implemented, notably Def 11 (preliminary surface Hadamard condition) and certain equations on p. 33. Explanations improved and typos fixed. This version corresponds largely to the published version in JCAP</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JCAP 01 (2023), 040 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1907.09960">arXiv:1907.09960</a> <span> [<a href="https://arxiv.org/pdf/1907.09960">pdf</a>, <a href="https://arxiv.org/ps/1907.09960">ps</a>, <a href="https://arxiv.org/format/1907.09960">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/10.1063/1.5122782">10.1063/1.5122782 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Semiclassical theories as initial value problems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Ju%C3%A1rez-Aubry%2C+B+A">Benito A. Ju谩rez-Aubry</a>, <a href="/search/gr-qc?searchtype=author&query=Miramontes%2C+T">Tonatiuh Miramontes</a>, <a href="/search/gr-qc?searchtype=author&query=Sudarsky%2C+D">Daniel Sudarsky</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="1907.09960v1-abstract-short" style="display: inline;"> Motivated by the initial value problem in semiclassical gravity, we study the initial value problem of a system consisting of a quantum scalar field weakly interacting with a classical one. The quantum field obeys a Klein-Gordon equation with a potential proportional to the classical field. The classical field obeys an inhomogeneous Klein-Gordon equation sourced by the renormalised expectation val… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.09960v1-abstract-full').style.display = 'inline'; document.getElementById('1907.09960v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1907.09960v1-abstract-full" style="display: none;"> Motivated by the initial value problem in semiclassical gravity, we study the initial value problem of a system consisting of a quantum scalar field weakly interacting with a classical one. The quantum field obeys a Klein-Gordon equation with a potential proportional to the classical field. The classical field obeys an inhomogeneous Klein-Gordon equation sourced by the renormalised expectation value of the squared quantum field in a Hadamard state, $\langle 唯| 桅^2 唯\rangle$. Thus, the system of equations for the scalar fields reminisces of the semi-classical Einstein field equations with a Klein-Gordon field, where classical geometry is sourced by the renormalised stress-energy tensor of the quantum field, and the Klein-Gordon equation depends on the metric explicitly. We show that a unique asymptotic solution for the system can be obtained perturbatively at any fixed finite order in the weak coupling from initial data provided that the interaction is switched on and off smoothly in a spacetime region to the future of the initial data surface. This allows one to provide "free" initial data for the decoupled system that guarantees that the Wightman function of the quantum field be of Hadamard form, and hence that the renormalised $\langle 唯| 桅^2 唯\rangle$ exist (in a perturbative sense) and be smooth. We comment on how to relax the switching of the interaction, which might be relevant for the corresponding problem in semiclassical gravity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.09960v1-abstract-full').style.display = 'none'; document.getElementById('1907.09960v1-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> 23 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2019. </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">37 pp</span> </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 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