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href="/nlab/show/geometry+of+physics">geometry of physics</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/books+and+reviews+in+mathematical+physics">books and reviews</a>, <a class="existingWikiWord" href="/nlab/show/physics+resources">physics resources</a> </li> </ul> <hr /> <a class="existingWikiWord" href="/nlab/show/theory+%28physics%29">theory (physics)</a>, <a class="existingWikiWord" href="/nlab/show/model+%28physics%29">model (physics)</a> <a class="existingWikiWord" href="/nlab/show/experiment">experiment</a>, <a class="existingWikiWord" href="/nlab/show/measurement">measurement</a>, <a class="existingWikiWord" href="/nlab/show/computable+physics">computable physics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/mechanics">mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/mass">mass</a>, <a class="existingWikiWord" href="/nlab/show/charge">charge</a>, <a class="existingWikiWord" href="/nlab/show/momentum">momentum</a>, <a class="existingWikiWord" href="/nlab/show/angular+momentum">angular momentum</a>, <a class="existingWikiWord" href="/nlab/show/moment+of+inertia">moment of inertia</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/dynamics+on+Lie+groups">dynamics on Lie groups</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/rigid+body+dynamics">rigid body dynamics</a></li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/field+%28physics%29">field (physics)</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Lagrangian+mechanics">Lagrangian mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/configuration+space">configuration space</a>, <a class="existingWikiWord" href="/nlab/show/state">state</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/action+functional">action functional</a>, <a class="existingWikiWord" href="/nlab/show/Lagrangian">Lagrangian</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/covariant+phase+space">covariant phase space</a>, <a class="existingWikiWord" href="/nlab/show/Euler-Lagrange+equations">Euler-Lagrange equations</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Hamiltonian+mechanics">Hamiltonian mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/phase+space">phase space</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/symplectic+geometry">symplectic geometry</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Poisson+manifold">Poisson manifold</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/symplectic+manifold">symplectic manifold</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/symplectic+groupoid">symplectic groupoid</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/multisymplectic+geometry">multisymplectic geometry</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/n-symplectic+manifold">n-symplectic manifold</a></li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/smooth+Lorentzian+manifold">smooth Lorentzian manifold</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/special+relativity">special relativity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/general+relativity">general relativity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/gravity">gravity</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>, <a class="existingWikiWord" href="/nlab/show/dilaton+gravity">dilaton gravity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a> </li> </ul> </li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/classical+field+theory">Classical field theory</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/classical+physics">classical physics</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/classical+mechanics">classical mechanics</a></li> <li><a class="existingWikiWord" href="/nlab/show/waves">waves</a> and <a class="existingWikiWord" href="/nlab/show/optics">optics</a></li> <li><a class="existingWikiWord" href="/nlab/show/thermodynamics">thermodynamics</a></li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+mechanics">Quantum Mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/quantum+mechanics+in+terms+of+dagger-compact+categories">in terms of ∞-compact categories</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+information">quantum information</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Hamiltonian+operator">Hamiltonian operator</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/density+matrix">density matrix</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Kochen-Specker+theorem">Kochen-Specker theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bell%27s+theorem">Bell's theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Gleason%27s+theorem">Gleason's theorem</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantization">Quantization</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/geometric+quantization">geometric quantization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/deformation+quantization">deformation quantization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/path+integral">path integral quantization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/semiclassical+approximation">semiclassical approximation</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">Quantum Field Theory</a> <ul> <li> Axiomatizations <ul> <li> <a class="existingWikiWord" href="/nlab/show/AQFT">algebraic QFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Wightman+axioms">Wightman axioms</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Haag-Kastler+axioms">Haag-Kastler axioms</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/operator+algebra">operator algebra</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/local+net">local net</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/conformal+net">conformal net</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Reeh-Schlieder+theorem">Reeh-Schlieder theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Osterwalder-Schrader+theorem">Osterwalder-Schrader theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/PCT+theorem">PCT theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bisognano-Wichmann+theorem">Bisognano-Wichmann theorem</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/modular+theory">modular theory</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/spin-statistics+theorem">spin-statistics theorem</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/boson">boson</a>, <a class="existingWikiWord" href="/nlab/show/fermion">fermion</a></li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/FQFT">functorial QFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/cobordism">cobordism</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/%28%E2%88%9E%2Cn%29-category+of+cobordisms">(∞,n)-category of cobordisms</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/cobordism+hypothesis">cobordism hypothesis</a>-theorem </li> <li> <a class="existingWikiWord" href="/nlab/show/extended+topological+quantum+field+theory">extended topological quantum field theory</a> </li> </ul> </li> </ul> </li> <li> Tools <ul> <li> <a class="existingWikiWord" href="/nlab/show/perturbative+quantum+field+theory">perturbative quantum field theory</a>, <a class="existingWikiWord" href="/nlab/show/vacuum">vacuum</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/effective+quantum+field+theory">effective quantum field theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/renormalization">renormalization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/BV-BRST+formalism">BV-BRST formalism</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/geometric+%E2%88%9E-function+theory">geometric ∞-function theory</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/particle+physics">particle physics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/phenomenology">phenomenology</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+%28in+particle+phyiscs%29">models</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/standard+model+of+particle+physics">standard model of particle physics</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/fields+and+quanta+-+table">fields and quanta</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/GUT">Grand Unified Theories</a>, <a class="existingWikiWord" href="/nlab/show/MSSM">MSSM</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/scattering+amplitude">scattering amplitude</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/on-shell+recursion">on-shell recursion</a>, <a class="existingWikiWord" href="/nlab/show/KLT+relations">KLT relations</a></li> </ul> </li> </ul> </li> <li> Structural phenomena <ul> <li> <a class="existingWikiWord" href="/nlab/show/universality+class">universality class</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+anomaly">quantum anomaly</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Green-Schwarz+mechanism">Green-Schwarz mechanism</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/instanton">instanton</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/spontaneously+broken+symmetry">spontaneously broken symmetry</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Kaluza-Klein+mechanism">Kaluza-Klein mechanism</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/integrable+systems">integrable systems</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/holonomic+quantum+fields">holonomic quantum fields</a> </li> </ul> </li> <li> Types of quantum field thories <ul> <li> <a class="existingWikiWord" href="/nlab/show/TQFT">TQFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/2d+TQFT">2d TQFT</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Dijkgraaf-Witten+theory">Dijkgraaf-Witten theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Chern-Simons+theory">Chern-Simons theory</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/TCFT">TCFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/A-model">A-model</a>, <a class="existingWikiWord" href="/nlab/show/B-model">B-model</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/homological+mirror+symmetry">homological mirror symmetry</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/QFT+with+defects">QFT with defects</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/conformal+field+theory">conformal field theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/%281%2C1%29-dimensional+Euclidean+field+theories+and+K-theory">(1,1)-dimensional Euclidean field theories and K-theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/%282%2C1%29-dimensional+Euclidean+field+theory">(2,1)-dimensional Euclidean field theory and elliptic cohomology</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/CFT">CFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/WZW+model">WZW model</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/6d+%282%2C0%29-supersymmetric+QFT">6d (2,0)-supersymmetric QFT</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/gauge+theory">gauge theory</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/field+strength">field strength</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/gauge+group">gauge group</a>, <a class="existingWikiWord" href="/nlab/show/gauge+transformation">gauge transformation</a>, <a class="existingWikiWord" href="/nlab/show/gauge+fixing">gauge fixing</a> </li> <li> examples <ul> <li><a class="existingWikiWord" href="/nlab/show/electromagnetic+field">electromagnetic field</a>, <a class="existingWikiWord" href="/nlab/show/QED">QED</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/electric+charge">electric charge</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/magnetic+charge">magnetic charge</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yang-Mills+field">Yang-Mills field</a>, <a class="existingWikiWord" href="/nlab/show/QCD">QCD</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Yang-Mills+theory">Yang-Mills theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/spinors+in+Yang-Mills+theory">spinors in Yang-Mills theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/topological+Yang-Mills+theory">topological Yang-Mills theory</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Kalb-Ramond+field">Kalb-Ramond field</a></li> <li><a class="existingWikiWord" href="/nlab/show/supergravity+C-field">supergravity C-field</a></li> <li><a class="existingWikiWord" href="/nlab/show/RR+field">RR field</a></li> <li><a class="existingWikiWord" href="/nlab/show/first-order+formulation+of+gravity">first-order formulation of gravity</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/general+covariance">general covariance</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/D%27Auria-Fre+formulation+of+supergravity">D'Auria-Fre formulation of supergravity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/gravity+as+a+BF-theory">gravity as a BF-theory</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/sigma-model">sigma-model</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/particle">particle</a>, <a class="existingWikiWord" href="/nlab/show/relativistic+particle">relativistic particle</a>, <a class="existingWikiWord" href="/nlab/show/fundamental+particle">fundamental particle</a>, <a class="existingWikiWord" href="/nlab/show/spinning+particle">spinning particle</a>, <a class="existingWikiWord" href="/nlab/show/superparticle">superparticle</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/string">string</a>, <a class="existingWikiWord" href="/nlab/show/spinning+string">spinning string</a>, <a class="existingWikiWord" href="/nlab/show/superstring">superstring</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/membrane">membrane</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/AKSZ+theory">AKSZ theory</a> </li> </ul> </li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/string+theory">String Theory</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/string+theory+results+applied+elsewhere">string theory results applied elsewhere</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/number+theory+and+physics">number theory and physics</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Riemann+hypothesis+and+physics">Riemann hypothesis and physics</a></li> </ul> </li> </ul> <div> <a href="/nlab/edit/physicscontents">Edit this sidebar</a> </div></div></div> </div> </div> The intention of this page is to list a wide choice of main books and comprehensive reviews in <a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical physics</a>. The irrelevant repetitions and minor, too specialized and obsolete books in any major respect should be avoided. We avoid references for quantum groups as they are many and the main ones can be found at the <a class="existingWikiWord" href="/nlab/show/quantum+group">quantum group</a> entry; similarly we avoided the relevant books on Kac-Moody algebras and groups but included the books on related VOAs and the Pressley-Segal book. <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#classical_mathematical_physics'>Classical mathematical physics</a></li> <li><a href='#classical_mechanics'>Classical mechanics</a></li> <li><a href='#mathematical_introduction_to_quantum_mechanics'>Mathematical introduction to quantum mechanics</a></li> <li><a href='#geometry_and_symmetries_in_classical_and_qm_quantization_but_no_qft'>Geometry and symmetries in classical and QM, quantization (but no QFT)</a></li> <li><a href='#lorentzian_geometry_and_general_relativity'>Lorentzian geometry and general relativity</a></li> <li><a href='#integrable_systems_and_solitons'>Integrable systems and solitons</a></li> <li><a href='#modern_mathematical_approaches_to_qft_and_strings'>Modern mathematical approaches to QFT and strings</a></li> <ul> <li><a href='#branes_mathematical_aspects'>Branes (mathematical aspects)</a></li> </ul> <li><a href='#conformal_field_theory_and_vertex_algebras'>Conformal field theory and vertex algebras</a></li> <li><a href='#axiomatic_quantumstatistical_field_theory_and_rigorous_approaches_to_path_integral'>Axiomatic quantum/statistical field theory and rigorous approaches to path integral</a></li> <li><a href='#other_reference_lists'>Other reference lists</a></li> </ul> </div> <h2 id="classical_mathematical_physics">Classical mathematical physics</h2> Here <a class="existingWikiWord" href="/nlab/show/PDEs">PDEs</a>, <a class="existingWikiWord" href="/nlab/show/differential+equation">ODE</a>s, and integral equation of mathematical physics, special functions, <a class="existingWikiWord" href="/nlab/show/generalized+function">generalized function</a>s, analytic functions, basic <a class="existingWikiWord" href="/nlab/show/functional+analysis">functional analysis</a>, potential theory: <ul> <li> R. Courant, <a class="existingWikiWord" href="/nlab/show/David+Hilbert">David Hilbert</a>, Methods of mathematical physics, 2 vols. </li> <li> P. M. Morse, H. Feshbach, Methods of theoretical physics I, II, <a href="http://www.feshbachpublishing.com">publisher</a> </li> <li> Michael Reed, Barry Simon, Methods of modern mathematical physics, 4 vols. (emphasis on functional analysis) </li> <li> V. Vladimirov, Equations of mathematical physics, Moscow, Izdatel’stvo Nauka, (1976. 528 p. Russian; English edition, Mir 198x); Generalized functions in mathematical physics, Moscow </li> </ul> Focus on <a class="existingWikiWord" href="/nlab/show/differential+geometry">differential geometry</a>: <ul> <li> <a class="existingWikiWord" href="/nlab/show/Yvonne+Choquet-Bruhat">Yvonne Choquet-Bruhat</a>, <a class="existingWikiWord" href="/nlab/show/C%C3%A9cile+DeWitt-Morette">Cécile DeWitt-Morette</a>, Analysis, manifolds and physics, North Holland (1982, 2001) [<a href="https://www.elsevier.com/books/analysis-manifolds-and-physics-revised-edition/choquet-bruhat/978-0-444-86017-0">ISBN:9780444860170</a>] </li> <li> <a class="existingWikiWord" href="/nlab/show/Mikhail+O.+Katanaev">Mikhail O. Katanaev</a>, Geometrical methods in mathematical physics (in Russian) [<a href="https://arxiv.org/abs/1311.0733">arXiv1311.0733</a>] </li> </ul> <h2 id="classical_mechanics">Classical mechanics</h2> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Vladimir+Arnold">Vladimir Arnold</a>, <a class="existingWikiWord" href="/nlab/show/Mathematical+methods+of+classical+mechanics">Mathematical methods of classical mechanics</a>, Springer (1989). </li> <li> <a class="existingWikiWord" href="/nlab/show/Michael+Spivak">Michael Spivak</a>, Physics for Mathematicians, Mechanics I, xvi + 733 pages, Publish or Perish 2010 <a href="http://olivier.thill.perso.neuf.fr/books/bospphma.htm">contents</a>, <a href="http://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322">amazon</a>; Elementary mechanics from a mathematician’s viewpoint, <a href="http://www.math.uga.edu/~shifrin/Spivak_physics.pdf">pdf</a> </li> <li> R. Abraham, J. Marsden, The Foundations of Mechanics, Benjamin Press, 1967, Addison-Wesley, 1978; large pdf 86 Mb free at <a href="http://resolver.caltech.edu/CaltechBOOK:1987.001">CaltechAuthors</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/William+Lawvere">William Lawvere</a>, <a class="existingWikiWord" href="/nlab/show/Stephen+Schanuel">Stephen Schanuel</a> (eds.), <a class="existingWikiWord" href="/nlab/show/Categories+in+Continuum+Physics">Categories in Continuum Physics</a>, Lectures given at a Workshop held at SUNY, Buffalo 1982, Lecture Notes in Mathematics 1174, 1986 </li> <li> <a class="existingWikiWord" href="/nlab/show/Vicente+Cort%C3%A9s">Vicente Cortés</a>, Alexander S. Haupt, Lecture Notes on Mathematical Methods of Classical Physics, (<a href="https://arxiv.org/abs/1612.03100">arXiv:1612.03100</a>) </li> </ul> <h2 id="mathematical_introduction_to_quantum_mechanics">Mathematical introduction to quantum mechanics</h2> On <a class="existingWikiWord" href="/nlab/show/quantum+mechanics">quantum mechanics</a>: <ul> <li> Anthony Sudbery, Quantum mechanics and the particles of nature: An outline for mathematicians </li> <li> <a class="existingWikiWord" href="/nlab/show/Leon+A.+Takhtajan">Leon A. Takhtajan</a>, <a class="existingWikiWord" href="/nlab/show/Quantum+mechanics+for+mathematicians">Quantum mechanics for mathematicians</a>, Graduate Studies in Mathematics 95, Amer. Math. Soc. 2008. </li> <li> Brian C. Hall, Quantum theory for mathematicians, Springer GTM 267 (has also a big chapter on geometric quantization) </li> </ul> <h2 id="geometry_and_symmetries_in_classical_and_qm_quantization_but_no_qft">Geometry and symmetries in classical and QM, quantization (but no QFT)</h2> In addition to the geometrically written titles under classical mechanics above, <ul> <li> Bernard F. Schutz, Geometrical methods of mathematical physics (elementary intro) <a href="http://www.amazon.com/Geometrical-Methods-Mathematical-Physics-Bernard/dp/0521298873">amazon</a>, <a href="http://books.google.hr/books?id=HAPMB2e643kC&lpg=PP1&dq=schutz%20geometrical%20methods&pg=PP1#v=onepage&q&f=false">google</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Peter+Olver">Peter Olver</a>, Equivalence, invariants, and symmetry, Cambridge Univ. Press 1995; Applications of Lie groups to differential equations, Springer. </li> <li> <a class="existingWikiWord" href="/nlab/show/Shlomo+Sternberg">Shlomo Sternberg</a>, Group theory and physics, Cambridge University Press 1994. </li> <li> <a class="existingWikiWord" href="/nlab/show/Victor+Guillemin">Victor Guillemin</a>, <a class="existingWikiWord" href="/nlab/show/Shlomo+Sternberg">Shlomo Sternberg</a>, Symplectic techniques in physics, Cambridge University Press (1990) </li> <li> <a class="existingWikiWord" href="/nlab/show/Theodore+Frankel">Theodore Frankel</a>, <a class="existingWikiWord" href="/nlab/show/The+Geometry+of+Physics+-+An+Introduction">The Geometry of Physics - An Introduction</a>, Cambridge Univ. Press </li> <li> <a class="existingWikiWord" href="/nlab/show/Chris+Isham">Chris Isham</a>, <a class="existingWikiWord" href="/nlab/show/Modern+Differential+Geometry+for+Physicists">Modern Differential Geometry for Physicists</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Klaas+Landsman">Klaas Landsman</a>, Mathematical topics between classical and quantum mechanics, Springer Monographs in Mathematics 1998. xx+529 pp. </li> <li> Sean Bates, <a class="existingWikiWord" href="/nlab/show/Alan+Weinstein">Alan Weinstein</a>, Lectures on the geometry of quantization, <a href="http://www.math.berkeley.edu/~alanw/GofQ.pdf">pdf</a> </li> <li> A. Cannas da Silva, A. Weinstein, Geometric models for noncommutative algebras, 1999, <a href="http://math.berkeley.edu/%7Ealanw/Models.pdf">pdf</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Nikolai+Reshetikhin">Nikolai Reshetikhin</a>, Lectures on quantization of gauge systems, <a href="http://arxiv.org/abs/1008.1411">arxiv/1008.1411</a> </li> </ul> <h2 id="lorentzian_geometry_and_general_relativity">Lorentzian geometry and general relativity</h2> Global aspects of the geometry of spacetimes: <ul> <li> John K. Beem, Paul E. Ehrlich, Kevin L. Easley, Global Lorentzian geometry (<a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0846.53001&format=complete">ZMATH</a>) (global aspects) </li> <li> Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 10, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1987, xii + 510 pp. (differential geometry of solutions to Einstein equations, constant negative curvature, classification results, encyclopaedic; for a review see <a href="http://projecteuclid.org/euclid.bams/1183554925">Bull. AMS</a> </li> </ul> After the introduction emphasis on asymptotics of spacetimes far from gravitation objects: <ul> <li>John Stewart, Advanced general relativity (<a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0752.53048&format=complete">ZMATH entry</a>)</li> </ul> Despite its title the next monograph does not just present the Kerr spacetime, it illustrates many core features of GR with the Kerr spacetime as the prominent example: <ul> <li>Barrett O’Neill, The geometry of Kerr black holes. (<a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0828.53078&format=complete">ZMATH</a>)</li> </ul> Here is an introduction to spinors in GR: <ul> <li>Peter O’Donnell, Introduction to 2-spinors in general relativity. (<a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1021.83001&format=complete">ZMATH</a>)</li> </ul> while the classic reference for this is: <ul> <li> Roger Penrose, Wolfgang Rindler, Spinors and spacetimes (2 vols, <a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0538.53024&format=complete">vol 1, ZMATH</a>) </li> <li> Eric Poisson, A relativist’s toolkit. The mathematics of black-hole mechanics. (<a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1058.83002&format=complete">ZMATH</a>) (computationally oriented) </li> </ul> See also the above book by Ward and Wells; and mainstream theoretical physics gravity textbooks by Misner, Thorne and Wheeler; Schutz; Landau-Lifschitz vol. 2; Wald; <a class="existingWikiWord" href="/nlab/show/Chandrasekhar">Chandrasekhar</a> etc. For the <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> see the appropriate chapters in the above listed collection by Deligne et al. or the references listed at <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>. <h2 id="integrable_systems_and_solitons">Integrable systems and solitons</h2> On <a class="existingWikiWord" href="/nlab/show/integrable+system">integrable system</a>s and <a class="existingWikiWord" href="/nlab/show/soliton">soliton</a>s: <ul> <li> O. Babelon, D. Bernard, M. Talon, Introduction to classical integrable systems, Cambridge Univ. Press 2003. </li> <li> T. Miwa, M. Jimbo, E. Date, Solitons: Differential equations, symmetries and infinite dimensional algebras, Cambridge Tracts in Mathematics 135, translated from Japanese by Miles Reid </li> <li> V.E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum inverse scattering method and correlation functions, Cambridge Univ. Press 1997. </li> <li> Ludwig D. Faddeev, Leon Takhtajan, Hamiltonian methods in the theory of solitons, Springer </li> </ul> <h2 id="modern_mathematical_approaches_to_qft_and_strings">Modern mathematical approaches to QFT and strings</h2> On <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a> and <a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a>: <ul> <li> Yvonne Choquet-Bruhat, Cecile Dewitt-Morette, Analysis, manifolds and physics, 1982 and 2001 </li> <li> Albert Schwartz, Quantum field theory and topology, Grundlehren der Math. Wissen. 307, Springer 1993. (translated from Russian original) </li> <li> Howard Georgi: Lie Algebras in Particle Physics. From isospin to unified theories. (<a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0505.00036&format=complete">ZMATH entry</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/Eberhard+Zeidler">Eberhard Zeidler</a>, Quantum field theory. A bridge between mathematicians and physicists. I: Basics in mathematics and physics. , II: Quantum electrodynamics </li> <li id="HenneauxTeitelboim"> <a class="existingWikiWord" href="/nlab/show/Marc+Henneaux">Marc Henneaux</a>, <a class="existingWikiWord" href="/nlab/show/Claudio+Teitelboim">Claudio Teitelboim</a>, <a class="existingWikiWord" href="/nlab/show/Quantization+of+Gauge+Systems">Quantization of Gauge Systems</a>, Princeton University Press 1992. </li> <li> Charles Nash, Differential topology and quantum field theory, Acad. Press 1991. </li> <li> P. Deligne, P. Etingof, D.S. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D.R. Morrison and E. Witten, eds. Quantum fields and strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (<a href="http://www.math.ias.edu/qft">web version</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/Gregory+L.+Naber">Gregory L. Naber</a>, Topology, Geometry and Gauge fields – Foundations, Texts in Applied Mathematics 25 (2011) [<a href="https://doi.org/10.1007/978-1-4419-7254-5">doi:10.1007/978-1-4419-7254-5</a>] </li> <li> <a class="existingWikiWord" href="/nlab/show/Gregory+L.+Naber">Gregory L. Naber</a>, Topology, Geometry and Gauge fields – Interactions, Applied Mathematical Sciences 141 (2011) [<a href="https://doi.org/10.1007/978-1-4419-7895-0">doi:10.1007/978-1-4419-7895-0</a>] </li> <li> <a class="existingWikiWord" href="/nlab/show/Mikio+Nakahara">Mikio Nakahara</a>, <a class="existingWikiWord" href="/nlab/show/Geometry%2C+Topology+and+Physics">Geometry, Topology and Physics</a> </li> <li> Marian Fecko, Differential geometry and Lie groups for physicists </li> <li> V. S. Varadarajan, Supersymmetry for mathematicians: an introduction, AMS and Courant Institute, 2004. </li> <li> R. S. Ward, R. O. Wells, Twistor geometry and field theory (CUP, 1990) </li> <li> R. E. Borcherds, A. Barnard, Lectures on QFT, <a href="http://arxiv.org/abs/math-ph/0204014">arxiv:math-ph/0204014</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Anton+Kapustin">Anton Kapustin</a>, Topological field theory, higher categories, and their applications, survey for ICM 2010, <a href="http://arxiv.org/abs/1004.2307">arxiv/1004.2307</a> </li> <li> Siddhartha Sen, <a class="existingWikiWord" href="/zoranskoda/show/Kumar+Gupta">Kumar Sankar Gupta</a>, <a class="existingWikiWord" href="/zoranskoda/show/Gupta-Sen+book">Many-body physics, topology and geometry</a> </li> </ul> <h3 id="branes_mathematical_aspects">Branes (mathematical aspects)</h3> <ul> <li> Paul Aspinwall, Tom Bridgeland, Alastair Craw, Michael R. Douglas, Mark Gross, Dirichlet branes and mirror symmetry, Amer. Math. Soc. Clay Math. Institute 2009. </li> <li> Hisham Sati, <a class="existingWikiWord" href="/nlab/show/Geometric+and+topological+structures+related+to+M-branes">Geometric and topological structures related to M-branes</a>, part I (<a href="http://arXiv.org/abs/1001.5020">arXiv:1001.5020</a>), part II: Twisted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>String</mi></mrow><annotation encoding="application/x-tex">String</annotation></semantics></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msup><mi>String</mi> <mi>c</mi></msup></mrow><annotation encoding="application/x-tex">String^c</annotation></semantics></math> structures (<a href="http://arxiv.org/abs/1007.5419">arxiv/1007.5419</a>); part III: Twisted higher structures (<a href="http://arxiv.org/abs/1008.1755">http://arxiv.org/abs/1008.1755</a>) </li> <li> A. N. Kapustin, <a class="existingWikiWord" href="/nlab/show/Dmitri+Orlov">D. O. Orlov</a>, Lectures on mirror symmetry, derived categories, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math>-branes, Russian Mathematical Surveys, 2004, 59:5, 907–940 (Russian version: <a href="http://www.mathnet.ru/php/getFT.phtml?jrnid=rm&paperid=772&volume=59&year=2004&issue=5&fpage=101&what=fullt&option_lang=eng">pdf</a>, [arxiv version: arxiv:math.AG/0308173).] </li> </ul> <h2 id="conformal_field_theory_and_vertex_algebras">Conformal field theory and vertex algebras</h2> On <a class="existingWikiWord" href="/nlab/show/conformal+field+theory">conformal field theory</a> and its chiral part (<a class="existingWikiWord" href="/nlab/show/vertex+operator+algebras">vertex operator algebras</a>, <a class="existingWikiWord" href="/nlab/show/chiral+algebras">chiral algebras</a>): <ul> <li> Edward Frenkel, David Ben-Zvi: Vertex algebras and algebraic curves, Math. Surveys and Monographs 88, AMS 2001, xii+348 pp. (Bull. AMS. <a href="http://www.ams.org/journals/bull/2002-39-04/S0273-0979-02-00955-2/S0273-0979-02-00955-2.pdf">review</a>, <a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1106.17035&format=complete">ZMATH entry</a>) </li> <li> Martin Schottenloher, A mathematical introduction to conformal field theory (CFT on the plane) </li> <li> Philippe Di Francesco, Pierre Mathieu, David Sénéchal, Conformal field theory, Springer 1997 (comprehensive textbook for theoretical physicists) </li> <li> Ralph Blumenhagen, Erik Plauschinn, Introduction to conformal field theory: with applications to string theory, Springer Lecture Notes in Physics (2011) </li> <li> V. Kac, Vertex algebras for beginners, Amer. Math. Soc. </li> <li> B. Bakalov, A. Kirillov, Lectures on tensor categories and modular functors, AMS, University Lecture Series, (2000) (<a href="http://www.math.sunysb.edu/~kirillov/tensor/tensor.html">web</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/Alexander+Beilinson">Alexander Beilinson</a>, <a class="existingWikiWord" href="/nlab/show/Vladimir+Drinfeld">Vladimir Drinfeld</a>, Chiral algebras, Colloqium Publications 51, Amer. Math. Soc. 2004, <a href="http://books.google.hr/books?id=yHZh3p-kFqQC&lpg=PP1&vq=%22Two-dimensional%20conformal%20geometry%20and%20vertex%20operator%20algebras%22&dq=isbn%3A0817638296&pg=PP1#v=onepage&q=%22Two-dimensional%20conformal%20geometry%20and%20vertex%20operator%20algebras%22&f=false">gbooks</a> </li> </ul> The related subject of positive energy representations for loop groups is represented in unavoidable reference <ul> <li>A. Pressley, G. Segal, Loop groups, Oxford Math. Monographs, 1986.</li> </ul> <h2 id="axiomatic_quantumstatistical_field_theory_and_rigorous_approaches_to_path_integral">Axiomatic quantum/statistical field theory and rigorous approaches to path integral</h2> <ul> <li> N. N. Bogoliubov, A. A. Logunov, I. T. Todorov, Introduction to axiomatic quantum field theory, 1975 </li> <li> R. Haag, Local quantum physics: fields, particles, algebras, Springer 1992 <a href="http://www.ams.org/mathscinet-getitem?mr=94d:81001">MR94d:81001</a>, 1996 <a href="http://www.ams.org/mathscinet-getitem?mr=98b:81001">MR98b:81001</a> </li> <li> Huzihiro Araki: Mathematical theory of quantum fields. Oxford University Press 1999 <a href="http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0998.81501&format=complete">ZMATH entry</a>. </li> <li> James Glimm, Arthur Jaffe, Quantum physics: a functional integral point of view, Springer </li> <li> Sergio Albeverio, Jens Erik Fenstad, Raphael Hoegh-Krohn, Nonstandard methods in stochastic analysis and mathematical physics, Acad. Press 1986 (there is also a Dover 2009 edition, and a 1990 Russian translation) </li> </ul> <h2 id="other_reference_lists">Other reference lists</h2> <ul> <li> <a href="http://en.wikibooks.org/wiki/Introduction_to_Mathematical_Physics/References">http://en.wikibooks.org/wiki/Introduction_to_Mathematical_Physics/References</a> (that list has mostly references in the area of theoretical physics and just a minority with rigor of mainstream mathematical physics) </li> <li> <a href="http://www.stringwiki.org/w/index.php?title=String_Theory_Wiki">www.stringwiki.org</a> – wiki contains entries on several dozens of string theory related topics, where each entry has several references, mainly papers available online </li> <li> <a class="existingWikiWord" href="/schreiber/show/Mathematical+Foundations+of+Quantum+Field+and+Perturbative+String+Theory">Mathematical Foundations of Quantum Field and Perturbative String Theory</a>, Proceedings of Symposia in Pure Mathematics 83, Amer. Math. Soc. (2011) </li> <li> MathOverflow discussion: <a href="http://mathoverflow.net/questions/191609/companion-to-theoretical-physics-for-working-mathematicians">Companion to theoretical physics for working mathematicians</a> </li> <li> reference list of Movshev’s sunysb <a href="http://www.math.sunysb.edu/~mmovshev/MAT570Spring2008/syllabusfinal.html">course on QM</a> </li> <li> geometrical background for <a class="existingWikiWord" href="/nlab/show/Anton+Kapustin">Anton Kapustin</a>‘s course at Caltech: <a href="http://theory.caltech.edu/~kapustin/Ph229/recbooks.html">list</a> </li> <li> John Baez: How to Learn Math and Physics (<a href="http://math.ucr.edu/home/baez/books.html">here</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/Fr%C3%A9d%C3%A9ric+Paugam">Frédéric Paugam</a>, Towards the mathematics of quantum field theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Volume 59, Springer (2014), (a draft formerly available <a href="http://people.math.jussieu.fr/~fpaugam/documents/enseignement/master-mathematical-physics.pdf">here</a>). </li> <li> <a class="existingWikiWord" href="/nlab/show/books+about+string+theory">books about string theory</a> </li> <li> various lectures notes in mathematical physics, Ulrich Theis’ list at <a href="http://www.personal.uni-jena.de/~p5thul2/notes/math.html">Jena</a> </li> </ul> <div class="property">category: <a class="category_link" href="/nlab/all_pages/reference">reference</a></div></body></html> </div> <div class="revisedby"> Last revised on January 26, 2024 at 05:16:58. 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