zbMATH — the first resource for mathematics

Mathematics Subject Classification – MSC2010

81-XX

Quantum theory 143938

81-00

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

81-01

Instructional exposition (textbooks, tutorial papers, etc.) 1645

81-02

Research exposition (monographs, survey articles) 3036

81-03

Historical (must also be assigned at least one classification number from Section 01) 1353

81-04

Explicit machine computation and programs (not the theory of computation or programming) 786

81-05

Experimental papers 278

81-06

Proceedings, conferences, collections, etc. 1932

81-08

Computational methods 1358

81Pxx

Axiomatics, foundations, philosophy 26519

81P05

General and philosophical 4682

81P10

Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15] 2211

81P13

Contextuality 176

81P15

Quantum measurement theory 5734

81P16

Quantum state spaces, operational and probabilistic concepts 579

81P20

Stochastic mechanics (including stochastic electrodynamics) 1440

81P40

Quantum coherence, entanglement, quantum correlations 5668

81P45

Quantum information, communication, networks [see also 94A15, 94A17] 3552

81P50

Quantum state estimation, approximate cloning 468

81P68

Quantum computation [See also 68Q05, 68Q12] 7918

81P70

Quantum coding (general) 673

81P94

Quantum cryptography [See also 94A60] 1566

81P99

None of the above, but in this section 595

81Qxx

General mathematical topics and methods in quantum theory 28816

81Q05

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 12151

81Q10

Selfadjoint operator theory in quantum theory, including spectral analysis 5915

81Q12

Non-selfadjoint operator theory in quantum theory 445

81Q15

Perturbation theories for operators and differential equations 1591

81Q20

Semiclassical techniques, including WKB and Maslov methods 3083

81Q30

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40] 913

81Q35

Quantum mechanics on special spaces: manifolds, fractals, graphs, etc. 926

81Q37

Quantum dots, waveguides, ratchets, etc. 635

81Q40

Bethe-Salpeter and other integral equations 351

81Q50

Quantum chaos [See also 37Dxx] 1943

81Q60

Supersymmetry and quantum mechanics 1949

81Q65

Alternative quantum mechanics 384

81Q70

Differential-geometric methods, including holonomy, Berry and Hannay phases, etc. 1246

81Q80

Special quantum systems, such as solvable systems 449

81Q93

Quantum control 631

81Q99

None of the above, but in this section 1229

81Rxx

Groups and algebras in quantum theory 25509

81R05

Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70] 4195

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] 4159

81R12

Relations with integrable systems [See also 17Bxx, 37J35] 3014

81R15

Operator algebra methods [See also 46Lxx, 81T05] 1486

81R20

Covariant wave equations 840

81R25

Spinor and twistor methods [See also 32L25] 1401

81R30

Coherent states [See also 22E45]; squeezed states [See also 81V80] 2980

81R40

Symmetry breaking 2747

81R50

Quantum groups and related algebraic methods [See also 16T20, 17B37] 5805

81R60

Noncommutative geometry 1413

81R99

None of the above, but in this section 221

81Sxx

General quantum mechanics and problems of quantization 12613

81S05

Canonical quantization, commutation relations and statistics 2252

81S10

Geometry and quantization, symplectic methods [See also 53D50] 2371

81S20

Stochastic quantization 349

81S22

Open systems, reduced dynamics, master equations, decoherence [See also 82C31] 1491

81S25

Quantum stochastic calculus 1893

81S30

Phase-space methods including Wigner distributions, etc. 1817

81S40

Path integrals [See also 58D30] 2519

81S99

None of the above, but in this section 630

81Txx

Quantum field theory; related classical field theories [See also 70Sxx] 54148

81T05

Axiomatic quantum field theory; operator algebras 2053

81T08

Constructive quantum field theory 1834

81T10

Model quantum field theories 3886

81T13

Yang-Mills and other gauge theories [See also 53C07, 58E15] 11970

81T15

Perturbative methods of renormalization 2786

81T16

Nonperturbative methods of renormalization 990

81T17

Renormalization group methods 2235

81T18

Feynman diagrams 1617

81T20

Quantum field theory on curved space backgrounds 5605

81T25

Quantum field theory on lattices 2393

81T27

Continuum limits 452

81T28

Thermal quantum field theory [see also 82B30] 505

81T30

String and superstring theories; other extended objects (e.g., branes) [See also 83E30] 14934

81T40

Two-dimensional field theories, conformal field theories, etc. 8803

81T45

Topological field theories [See also 57R56, 58Dxx] 1422

81T50

Anomalies 1337

81T55

Casimir effect 344

81T60

Supersymmetric field theories 9608

81T70

Quantization in field theory; cohomological methods [See also 58D29] 2063

81T75

Noncommutative geometry methods [See also 46L85, 46L87, 58B34] 1874

81T80

Simulation and numerical modeling 1207

81T99

None of the above, but in this section 1019

81Uxx

Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40] 8352

81U05

$2$-body potential scattering theory [See also 34E20 for WKB methods] 2612

81U10

$n$-body potential scattering theory 834

81U15

Exactly and quasi-solvable systems 941

81U20

$S$-matrix theory, etc. 1386

81U30

Dispersion theory, dispersion relations 270

81U35

Inelastic and multichannel scattering 648

81U40

Inverse scattering problems 1014

81U99

None of the above, but in this section 1151

81Vxx

Applications to specific physical systems 31715

81V05

Strong interaction, including quantum chromodynamics 5454

81V10

Electromagnetic interaction; quantum electrodynamics 3665

81V15

Weak interaction 1278

81V17

Gravitational interaction [See also 83Cxx and 83Exx] 2325

81V19

Other fundamental interactions 119

81V22

Unified theories 4093

81V25

Other elementary particle theory 1315

81V35

Nuclear physics 4083

81V45

Atomic physics 2669

81V55

Molecular physics [See also 92E10] 2438

81V65

Quantum dots [See also 82D20] 269

81V70

Many-body theory; quantum Hall effect 4178

81V80

Quantum optics 4948

81V99

None of the above, but in this section 616

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Mathematics Subject Classification – MSC2010

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