zbMATH — the first resource for mathematics

Mathematics Subject Classification – MSC2010

81-XX

Quantum theory 145926

81-00

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

81-01

Instructional exposition (textbooks, tutorial papers, etc.) 1675

81-02

Research exposition (monographs, survey articles) 3062

81-03

Historical (must also be assigned at least one classification number from Section 01) 1363

81-04

Explicit machine computation and programs (not the theory of computation or programming) 788

81-05

Experimental papers 282

81-06

Proceedings, conferences, collections, etc. 1942

81-08

Computational methods 1365

81Pxx

Axiomatics, foundations, philosophy 26922

81P05

General and philosophical 4734

81P10

Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15] 2225

81P13

Contextuality 180

81P15

Quantum measurement theory 5818

81P16

Quantum state spaces, operational and probabilistic concepts 598

81P20

Stochastic mechanics (including stochastic electrodynamics) 1446

81P40

Quantum coherence, entanglement, quantum correlations 5814

81P45

Quantum information, communication, networks [see also 94A15, 94A17] 3661

81P50

Quantum state estimation, approximate cloning 484

81P68

Quantum computation [See also 68Q05, 68Q12] 8004

81P70

Quantum coding (general) 686

81P94

Quantum cryptography [See also 94A60] 1607

81P99

None of the above, but in this section 597

81Qxx

General mathematical topics and methods in quantum theory 29083

81Q05

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 12245

81Q10

Selfadjoint operator theory in quantum theory, including spectral analysis 5963

81Q12

Non-selfadjoint operator theory in quantum theory 455

81Q15

Perturbation theories for operators and differential equations 1602

81Q20

Semiclassical techniques, including WKB and Maslov methods 3103

81Q30

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40] 936

81Q35

Quantum mechanics on special spaces: manifolds, fractals, graphs, etc. 957

81Q37

Quantum dots, waveguides, ratchets, etc. 641

81Q40

Bethe-Salpeter and other integral equations 355

81Q50

Quantum chaos [See also 37Dxx] 1953

81Q60

Supersymmetry and quantum mechanics 1961

81Q65

Alternative quantum mechanics 394

81Q70

Differential-geometric methods, including holonomy, Berry and Hannay phases, etc. 1264

81Q80

Special quantum systems, such as solvable systems 462

81Q93

Quantum control 642

81Q99

None of the above, but in this section 1229

81Rxx

Groups and algebras in quantum theory 25783

81R05

Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70] 4234

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] 4190

81R12

Relations with integrable systems [See also 17Bxx, 37J35] 3065

81R15

Operator algebra methods [See also 46Lxx, 81T05] 1498

81R20

Covariant wave equations 847

81R25

Spinor and twistor methods [See also 32L25] 1427

81R30

Coherent states [See also 22E45]; squeezed states [See also 81V80] 3023

81R40

Symmetry breaking 2802

81R50

Quantum groups and related algebraic methods [See also 16T20, 17B37] 5830

81R60

Noncommutative geometry 1422

81R99

None of the above, but in this section 223

81Sxx

General quantum mechanics and problems of quantization 12738

81S05

Canonical quantization, commutation relations and statistics 2269

81S10

Geometry and quantization, symplectic methods [See also 53D50] 2385

81S20

Stochastic quantization 352

81S22

Open systems, reduced dynamics, master equations, decoherence [See also 82C31] 1533

81S25

Quantum stochastic calculus 1911

81S30

Phase-space methods including Wigner distributions, etc. 1839

81S40

Path integrals [See also 58D30] 2532

81S99

None of the above, but in this section 629

81Txx

Quantum field theory; related classical field theories [See also 70Sxx] 54997

81T05

Axiomatic quantum field theory; operator algebras 2059

81T08

Constructive quantum field theory 1836

81T10

Model quantum field theories 3950

81T13

Yang-Mills and other gauge theories [See also 53C07, 58E15] 12145

81T15

Perturbative methods of renormalization 2817

81T16

Nonperturbative methods of renormalization 1008

81T17

Renormalization group methods 2272

81T18

Feynman diagrams 1653

81T20

Quantum field theory on curved space backgrounds 5644

81T25

Quantum field theory on lattices 2426

81T27

Continuum limits 457

81T28

Thermal quantum field theory [see also 82B30] 517

81T30

String and superstring theories; other extended objects (e.g., branes) [See also 83E30] 15126

81T40

Two-dimensional field theories, conformal field theories, etc. 8980

81T45

Topological field theories [See also 57R56, 58Dxx] 1453

81T50

Anomalies 1359

81T55

Casimir effect 357

81T60

Supersymmetric field theories 9831

81T70

Quantization in field theory; cohomological methods [See also 58D29] 2089

81T75

Noncommutative geometry methods [See also 46L85, 46L87, 58B34] 1895

81T80

Simulation and numerical modeling 1217

81T99

None of the above, but in this section 1021

81Uxx

Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40] 8451

81U05

$2$-body potential scattering theory [See also 34E20 for WKB methods] 2656

81U10

$n$-body potential scattering theory 840

81U15

Exactly and quasi-solvable systems 948

81U20

$S$-matrix theory, etc. 1399

81U30

Dispersion theory, dispersion relations 272

81U35

Inelastic and multichannel scattering 656

81U40

Inverse scattering problems 1022

81U99

None of the above, but in this section 1162

81Vxx

Applications to specific physical systems 32125

81V05

Strong interaction, including quantum chromodynamics 5517

81V10

Electromagnetic interaction; quantum electrodynamics 3710

81V15

Weak interaction 1286

81V17

Gravitational interaction [See also 83Cxx and 83Exx] 2371

81V19

Other fundamental interactions 128

81V22

Unified theories 4146

81V25

Other elementary particle theory 1353

81V35

Nuclear physics 4130

81V45

Atomic physics 2690

81V55

Molecular physics [See also 92E10] 2454

81V65

Quantum dots [See also 82D20] 271

81V70

Many-body theory; quantum Hall effect 4228

81V80

Quantum optics 5013

81V99

None of the above, but in this section 621

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Mathematics Subject Classification – MSC2010

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