nLab
mathematical physics

Skip the Navigation Links | Home Page | All Pages | Recently Revised | Authors | Feeds | Export |

Context

Physics

physics, mathematical physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

Mathematics

Contents

Idea

Mathematical physics is a discipline at the interface of mathematics and physics, concerned with developing mathematical models of physical phenomena and mathematical apparatus arising or needed in such models. It intersects with theoretical physics which deals with theoretical arguments in consideration of physical phenomena and the development of models of known and of conjectured physics; theoretical physics is in a sense wider as it deals also with interpretations, non-rigorous and sometimes speculative argument from experiments or from rough comparisons of different models and various experimental data, not entering or forming together a necessarily compatible mathematical entity. For example, the calculations of fitting parameters and adjusting models to complicated experimental data, called the phenomenology is part of the work of a theoretical physicist, but most such work is not nowadays considered to belong to mathematical physics, unless one is developing a really new mathematical model or tool for such work.

In the famous list of Hilbert's problems, the sixth problem states:

6. Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.

More recently, one also sometimes uses a less familiar term physical mathematics for the study of mathematical constructions inspired by models of theoretical physics; thus the final aim may be more mathematical (say finding a new topological invariant using physical intuition) than in the mathematical physics. However there is no clean boundary and to some extent the two notions are interchangeable.

See the related, but disputable notion of applied mathematics.

A historically inclined article on mathematical physics is featured on wikipedia.

For an extensive list of literature see

Further related entries include

Revised on May 10, 2013 18:28:35 by Urs Schreiber (82.169.65.155)
Edit | Back in time (7 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: HomePage, physics, BV-BRST formalism, brane, conformal field theory, AQFT, quantum field theory, FQFT, smooth Lorentzian space, physicscontents, topological T-duality, T-duality, sigma-model, GUT, string theory, higher category theory and physics, path integral, Dijkgraaf-Witten theory, orientifold, Green-Schwarz mechanism, FFRS-formalism, topological quantum field theory, quantum anomaly, QFT with defects, gauge theory, electromagnetism, electromagnetic field, Kalb-Ramond field, electric charge, magnetic charge, field strength, Yang-Mills theory, Yang-Mills field, integrable system, quantization, geometric quantization, BPS state, extended topological quantum field theory, Maxim Kontsevich, classical physics, classical mechanics, force, wave, Yuri Manin, Alain Connes, D'Auria-Fre formulation of supergravity, supergravity, classical field theory, Supergravity and Superstrings - A Geometric Perspective, Poisson sigma-model, quantum mechanics, action functional, supersymmetry, Lagrangian, Euler-Lagrange equation, Jordan algebra, Chern-Simons theory, quantum harmonic oscillator, perturbation theory, renormalization, Hamiltonian, gravity, first-order formulation of gravity, Plebanski formulation of gravity, landscape of string theory vacua, Hamiltonian mechanics, multisymplectic geometry, classical limit, thermodynamics, dilaton, gauge fixing, Shahn Majid, target space, S-duality, net of C-star-systems, conformal net, Seiberg-Witten theory, Haag-Kastler axioms, Topological Quantum Field Theories from Compact Lie Groups, Richard Borcherds, entanglement, Wightman axioms, quantum operation, modular theory, supersymmetric quantum mechanics, topological Yang-Mills theory, density matrix, quantum information, Maslov index, Osterwalder-Schrader theorem, superselection theory, finite quantum mechanics in terms of dagger-compact categories, Geometric and topological structures related to M-branes, semiclassical approximation, Stokes phenomenon, deformation quantization, quantum state, Kerr spacetime, standard model of particle physics, observable, phase space, mathematical physics, The Dirac Electron, variational calculus, DHR category, Gleason's theorem, books and reviews in mathematical physics, Peter Bantay, special relativity, Kochen-Specker theorem, spin-statistics theorem, Reeh-Schlieder theorem, general relativity, 2d TQFT, A-model, B-model, state, Fell's theorem, black hole, fermion, boson, gauge group, Dirac charge quantization and generalized differential cohomology, conserved current, AdS-CFT, Courant sigma-model, Bekenstein-Hawking entropy, generalized second law of thermodynamics, phenomenology, Wess-Zumino-Witten model, Schwarzschild spacetime, 11-dimensional supergravity, Andrey Lazarev, dual heterotic string theory, variational bicomplex, Calabi-Yau object, quantum gravity, Einstein-Hilbert action, formal noncommutative symplectic geometry, Kaluza-Klein mechanism, gauge transformation, math resources by individuals, gravitino, graviton, BF-theory, cosmological constant, SCFT, electric-magnetic duality, quantization via the A-model, holographic principle, Mathematical Theory of Quantum Fields, quantum electrodynamics, relativistic particle, Green-Schwarz action functional, Stone-von Neumann theorem, mechanical system, Yetter model, superparticle, Landau-Ginzburg model, second quantization, heterotic string theory, kinematics and dynamics, S-matrix, applied mathematics, Vladimir Turaev, Haag's theorem, causal locality, string, sewing constraint, photon, time slice axiom, charge of a conserved current, picture of mechanics, path integral as a pull-push transform, Noether's theorem, reductions deformations resolutions in physics, spinning particle, Peierls bracket, Mathematical Topics Between Classical and Quantum Mechanics, Renormalization and Effective Field Theory, configuration space, effective quantum field theory, Quantization of Gauge Systems, Noether identities, gaugino, Bohr topos, Gruppenpest, gluon, gauge boson, Three Roles of Quantum Field Theory, fermionic path integral, worldvolume, background field, particle, timelike curve, Lorentz force, Nambu-Goto action, differential T-duality, Einstein equation, fundamental particle, superstring, Fermi theory of beta decay, Quantum Fields and Strings, second law of thermodynamics, Cauchy surface, self-dual higher gauge theory, what to contribute, mechanics, QCD, Dirac interaction picture, classical state, Jordan-Lie-Banach algebra, Local Quantum Physics -- Fields, Particles, Algebras, spinning string, supersymmetry and Calabi-Yau manifolds, spontaneously broken symmetry, sigma-model -- exposition of classical sigma-models, sigma-model -- exposition of higher gauge theories as sigma-models, sigma-model -- exposition of quantum sigma-models, sigma-model -- exposition of a general abstract formulation, sigma-model -- exposition of second quantization of sigma-models, criticism of string theory, 4-dimensional supergravity, black brane, higher dimensional Chern-Simons theory, c-theorem, contents of contents, hole argument, Kapustin-Witten TQFT, instanton, 3-dimensional supergravity, Yang-Mills instanton, moment of inertia, 6d Chern-Simons theory, vacuum, 6d (2,0)-supersymmetric QFT, universality class, Geometric Algebra, rigid body dynamics, angular momentum, angular velocity, Euler-Arnold equation, Foundations of Mechanics, Hamiltonian dynamics on Lie groups, 3d quantum gravity, symplectic infinity-groupoid, geometric quantization of symplectic groupoids, Wick's lemma, Paul Dedecker, event horizon, Seiberg duality, counterterm, Steady State, effective action functional, collective field theory, false vacuum, flux, higher spin gauge theory, super Yang-Mills theory, 7-dimensional supergravity, N=4 D=4 super Yang-Mills theory, gauged supergravity, higher gauge field, physics resources, Feynman diagram, higher dimensional WZW model, 1-dimensional Chern-Simons theory, 4d WZW model, quantum lattice system, minimal coupling, Kirchhoff's laws, Born-Oppenheimer approximation, on-shell recursion, Freund-Rubin compactification, p-adic physics, quantum observable, coset WZW model, 1d WZW model, quantum hadrodynamics, braid group statistics, M-theory on G2-manifolds, observable universe, N=2 D=4 super Yang-Mills theory, N=4 D=3 super Yang-Mills theory, 3d Chern-Simons theory, teleparallel gravity, thermodynamic limit, Planck's constant, general covariance, quantum cosmology, technicolor, string phenomenology, Higgs field, The Geometry of Physics - An Introduction, Maxwell's equations, Harmonic oscillator, KLT relations, AGT correspondence, Einstein-Yang-Mills-Dirac-Higgs theory, C-star algebraic deformation quantization, Dirac charge quantization, kinetic action, instanton in QCD, G2-MSSM, magnetic field, MSSM, holomorphic Chern-Simons theory, cosmology, moduli stabilization, scattering amplitude, Turaev-Viro model, standard model of cosmology, open/closed string duality, model (in theoretical physics), particle physics, string theory results applied elsewhere, twistor string theory, quark-gluon plasma, cosmic inflation, Einstein-Maxwell theory, cosmic microwave background radiation, geometric quantization by push-forward, dark matter, higher gauge transformation, Einstein-Yang-Mills theory, geometry of physics, theory (physics), matter, confinement, virtual particle, electric field, Liouville integrable system, field (physics), Levin-Wen model, prequantum field theory, quark, QFT on non-commutative spacetime, MOND, BPTS-instanton, nuclear force, superposition, Aharonov-Bohm effect, ghost field, duality in physics, 7d Chern-Simons theory, electromagnetic potential, continuum mechanics, 5d Chern-Simons theory, self-dual Yang-Mills theory, electromagnetic field strength, higgsino, 2d Chern-Simons theory, electron, geometric quantization of non-integral forms, prequantum 0-bundle, Einstein-Yang-Mills-Dirac theory, neutrino, electroweak field, interaction, 4d Chern-Simons theory, Guillemin-Sternberg geometric quantization conjecture, free field theory, extended Lagrangian, renormalization scheme, Factorization algebras in perturbative quantum field theory, Moyal quantization, Chern-Simons invariant, field bundle, effect algebra, local quantum field theory, principle of least action, light, scalar field, Big Bang, W-boson, extended geometric quantization of 2d Chern-Simons theory, quantum decoherence, Hilbert's sixth problem, 4d TQFT, gravitational constant, semiclassical state, phase and phase space in physics, 1d Dijkgraaf-Witten theory