zbMATH — the first resource for mathematics

Mathematics Subject Classification – MSC2010

81-XX

Quantum theory 142602

81-00

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

81-01

Instructional exposition (textbooks, tutorial papers, etc.) 1636

81-02

Research exposition (monographs, survey articles) 3024

81-03

Historical (must also be assigned at least one classification number from Section 01) 1351

81-04

Explicit machine computation and programs (not the theory of computation or programming) 785

81-05

Experimental papers 278

81-06

Proceedings, conferences, collections, etc. 1924

81-08

Computational methods 1353

81Pxx

Axiomatics, foundations, philosophy 26055

81P05

General and philosophical 4642

81P10

Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15] 2194

81P13

Contextuality 172

81P15

Quantum measurement theory 5659

81P16

Quantum state spaces, operational and probabilistic concepts 559

81P20

Stochastic mechanics (including stochastic electrodynamics) 1435

81P40

Quantum coherence, entanglement, quantum correlations 5460

81P45

Quantum information, communication, networks [see also 94A15, 94A17] 3413

81P50

Quantum state estimation, approximate cloning 456

81P68

Quantum computation [See also 68Q05, 68Q12] 7838

81P70

Quantum coding (general) 647

81P94

Quantum cryptography [See also 94A60] 1490

81P99

None of the above, but in this section 593

81Qxx

General mathematical topics and methods in quantum theory 28573

81Q05

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 12066

81Q10

Selfadjoint operator theory in quantum theory, including spectral analysis 5870

81Q12

Non-selfadjoint operator theory in quantum theory 435

81Q15

Perturbation theories for operators and differential equations 1580

81Q20

Semiclassical techniques, including WKB and Maslov methods 3047

81Q30

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40] 908

81Q35

Quantum mechanics on special spaces: manifolds, fractals, graphs, etc. 907

81Q37

Quantum dots, waveguides, ratchets, etc. 623

81Q40

Bethe-Salpeter and other integral equations 349

81Q50

Quantum chaos [See also 37Dxx] 1933

81Q60

Supersymmetry and quantum mechanics 1943

81Q65

Alternative quantum mechanics 376

81Q70

Differential-geometric methods, including holonomy, Berry and Hannay phases, etc. 1238

81Q80

Special quantum systems, such as solvable systems 441

81Q93

Quantum control 609

81Q99

None of the above, but in this section 1224

81Rxx

Groups and algebras in quantum theory 25329

81R05

Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70] 4172

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] 4144

81R12

Relations with integrable systems [See also 17Bxx, 37J35] 2986

81R15

Operator algebra methods [See also 46Lxx, 81T05] 1477

81R20

Covariant wave equations 835

81R25

Spinor and twistor methods [See also 32L25] 1378

81R30

Coherent states [See also 22E45]; squeezed states [See also 81V80] 2936

81R40

Symmetry breaking 2730

81R50

Quantum groups and related algebraic methods [See also 16T20, 17B37] 5787

81R60

Noncommutative geometry 1395

81R99

None of the above, but in this section 220

81Sxx

General quantum mechanics and problems of quantization 12498

81S05

Canonical quantization, commutation relations and statistics 2234

81S10

Geometry and quantization, symplectic methods [See also 53D50] 2362

81S20

Stochastic quantization 344

81S22

Open systems, reduced dynamics, master equations, decoherence [See also 82C31] 1459

81S25

Quantum stochastic calculus 1882

81S30

Phase-space methods including Wigner distributions, etc. 1786

81S40

Path integrals [See also 58D30] 2501

81S99

None of the above, but in this section 629

81Txx

Quantum field theory; related classical field theories [See also 70Sxx] 53753

81T05

Axiomatic quantum field theory; operator algebras 2046

81T08

Constructive quantum field theory 1832

81T10

Model quantum field theories 3839

81T13

Yang-Mills and other gauge theories [See also 53C07, 58E15] 11892

81T15

Perturbative methods of renormalization 2766

81T16

Nonperturbative methods of renormalization 968

81T17

Renormalization group methods 2211

81T18

Feynman diagrams 1601

81T20

Quantum field theory on curved space backgrounds 5580

81T25

Quantum field theory on lattices 2377

81T27

Continuum limits 450

81T28

Thermal quantum field theory [see also 82B30] 500

81T30

String and superstring theories; other extended objects (e.g., branes) [See also 83E30] 14886

81T40

Two-dimensional field theories, conformal field theories, etc. 8686

81T45

Topological field theories [See also 57R56, 58Dxx] 1404

81T50

Anomalies 1312

81T55

Casimir effect 334

81T60

Supersymmetric field theories 9529

81T70

Quantization in field theory; cohomological methods [See also 58D29] 2053

81T75

Noncommutative geometry methods [See also 46L85, 46L87, 58B34] 1871

81T80

Simulation and numerical modeling 1198

81T99

None of the above, but in this section 1016

81Uxx

Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40] 8282

81U05

$2$-body potential scattering theory [See also 34E20 for WKB methods] 2583

81U10

$n$-body potential scattering theory 827

81U15

Exactly and quasi-solvable systems 938

81U20

$S$-matrix theory, etc. 1378

81U30

Dispersion theory, dispersion relations 265

81U35

Inelastic and multichannel scattering 641

81U40

Inverse scattering problems 1006

81U99

None of the above, but in this section 1143

81Vxx

Applications to specific physical systems 31455

81V05

Strong interaction, including quantum chromodynamics 5409

81V10

Electromagnetic interaction; quantum electrodynamics 3616

81V15

Weak interaction 1265

81V17

Gravitational interaction [See also 83Cxx and 83Exx] 2306

81V19

Other fundamental interactions 117

81V22

Unified theories 4074

81V25

Other elementary particle theory 1301

81V35

Nuclear physics 4060

81V45

Atomic physics 2648

81V55

Molecular physics [See also 92E10] 2424

81V65

Quantum dots [See also 82D20] 262

81V70

Many-body theory; quantum Hall effect 4140

81V80

Quantum optics 4896

81V99

None of the above, but in this section 616

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Mathematics Subject Classification – MSC2010

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