zbMATH — the first resource for mathematics

Mathematics Subject Classification – MSC2010

81-XX

Quantum theory 147064

81-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 28

81-01

Instructional exposition (textbooks, tutorial papers, etc.) 1694

81-02

Research exposition (monographs, survey articles) 3082

81-03

Historical (must also be assigned at least one classification number from Section 01) 1371

81-04

Explicit machine computation and programs (not the theory of computation or programming) 790

81-05

Experimental papers 289

81-06

Proceedings, conferences, collections, etc. 1953

81-08

Computational methods 1372

81Pxx

Axiomatics, foundations, philosophy 27251

81P05

General and philosophical 4775

81P10

Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15] 2244

81P13

Contextuality 184

81P15

Quantum measurement theory 5891

81P16

Quantum state spaces, operational and probabilistic concepts 630

81P20

Stochastic mechanics (including stochastic electrodynamics) 1447

81P40

Quantum coherence, entanglement, quantum correlations 5943

81P45

Quantum information, communication, networks [see also 94A15, 94A17] 3748

81P50

Quantum state estimation, approximate cloning 500

81P68

Quantum computation [See also 68Q05, 68Q12] 8090

81P70

Quantum coding (general) 700

81P94

Quantum cryptography [See also 94A60] 1647

81P99

None of the above, but in this section 597

81Qxx

General mathematical topics and methods in quantum theory 29312

81Q05

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 12338

81Q10

Selfadjoint operator theory in quantum theory, including spectral analysis 5999

81Q12

Non-selfadjoint operator theory in quantum theory 476

81Q15

Perturbation theories for operators and differential equations 1613

81Q20

Semiclassical techniques, including WKB and Maslov methods 3120

81Q30

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40] 948

81Q35

Quantum mechanics on special spaces: manifolds, fractals, graphs, etc. 975

81Q37

Quantum dots, waveguides, ratchets, etc. 648

81Q40

Bethe-Salpeter and other integral equations 356

81Q50

Quantum chaos [See also 37Dxx] 1967

81Q60

Supersymmetry and quantum mechanics 1971

81Q65

Alternative quantum mechanics 404

81Q70

Differential-geometric methods, including holonomy, Berry and Hannay phases, etc. 1267

81Q80

Special quantum systems, such as solvable systems 478

81Q93

Quantum control 656

81Q99

None of the above, but in this section 1229

81Rxx

Groups and algebras in quantum theory 25987

81R05

Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70] 4266

81R10

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70] 4216

81R12

Relations with integrable systems [See also 17Bxx, 37J35] 3109

81R15

Operator algebra methods [See also 46Lxx, 81T05] 1514

81R20

Covariant wave equations 859

81R25

Spinor and twistor methods [See also 32L25] 1453

81R30

Coherent states [See also 22E45]; squeezed states [See also 81V80] 3032

81R40

Symmetry breaking 2833

81R50

Quantum groups and related algebraic methods [See also 16T20, 17B37] 5853

81R60

Noncommutative geometry 1433

81R99

None of the above, but in this section 224

81Sxx

General quantum mechanics and problems of quantization 12831

81S05

Canonical quantization, commutation relations and statistics 2285

81S10

Geometry and quantization, symplectic methods [See also 53D50] 2398

81S20

Stochastic quantization 353

81S22

Open systems, reduced dynamics, master equations, decoherence [See also 82C31] 1563

81S25

Quantum stochastic calculus 1923

81S30

Phase-space methods including Wigner distributions, etc. 1854

81S40

Path integrals [See also 58D30] 2549

81S99

None of the above, but in this section 630

81Txx

Quantum field theory; related classical field theories [See also 70Sxx] 55540

81T05

Axiomatic quantum field theory; operator algebras 2069

81T08

Constructive quantum field theory 1839

81T10

Model quantum field theories 4007

81T13

Yang-Mills and other gauge theories [See also 53C07, 58E15] 12209

81T15

Perturbative methods of renormalization 2848

81T16

Nonperturbative methods of renormalization 1026

81T17

Renormalization group methods 2305

81T18

Feynman diagrams 1675

81T20

Quantum field theory on curved space backgrounds 5673

81T25

Quantum field theory on lattices 2458

81T27

Continuum limits 462

81T28

Thermal quantum field theory [see also 82B30] 531

81T30

String and superstring theories; other extended objects (e.g., branes) [See also 83E30] 15228

81T40

Two-dimensional field theories, conformal field theories, etc. 9140

81T45

Topological field theories [See also 57R56, 58Dxx] 1491

81T50

Anomalies 1388

81T55

Casimir effect 362

81T60

Supersymmetric field theories 9951

81T70

Quantization in field theory; cohomological methods [See also 58D29] 2095

81T75

Noncommutative geometry methods [See also 46L85, 46L87, 58B34] 1901

81T80

Simulation and numerical modeling 1223

81T99

None of the above, but in this section 1023

81Uxx

Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40] 8529

81U05

$2$-body potential scattering theory [See also 34E20 for WKB methods] 2686

81U10

$n$-body potential scattering theory 843

81U15

Exactly and quasi-solvable systems 954

81U20

$S$-matrix theory, etc. 1421

81U30

Dispersion theory, dispersion relations 273

81U35

Inelastic and multichannel scattering 662

81U40

Inverse scattering problems 1025

81U99

None of the above, but in this section 1172

81Vxx

Applications to specific physical systems 32404

81V05

Strong interaction, including quantum chromodynamics 5566

81V10

Electromagnetic interaction; quantum electrodynamics 3750

81V15

Weak interaction 1300

81V17

Gravitational interaction [See also 83Cxx and 83Exx] 2398

81V19

Other fundamental interactions 138

81V22

Unified theories 4174

81V25

Other elementary particle theory 1375

81V35

Nuclear physics 4160

81V45

Atomic physics 2704

81V55

Molecular physics [See also 92E10] 2473

81V65

Quantum dots [See also 82D20] 273

81V70

Many-body theory; quantum Hall effect 4261

81V80

Quantum optics 5055

81V99

None of the above, but in this section 621

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Mathematics Subject Classification – MSC2010

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