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Mathematics Subject Classification – MSC2020

81-XX

Quantum theory 153802

81-00

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to quantum theory 28

81-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory 1765

81-02

Research exposition (monographs, survey articles) pertaining to quantum theory 3180

81-03

History of quantum theory [Consider also classification numbers pertaining to Section 01-XX] 1416

81-04

Software, source code, etc. for problems pertaining to quantum theory 803

81-05

Experimental work for problems pertaining to quantum theory 298

81-06

Proceedings, conferences, collections, etc. pertaining to quantum theory 1999

81-08

Computational methods for problems pertaining to quantum theory 1418

81-10

Mathematical modeling or simulation for problems pertaining to quantum theory 2

81-11

Research data for problems pertaining to quantum theory 0

81Pxx

Foundations, quantum information and its processing, quantum axioms, and philosophy 29124

81P05

General and philosophical questions in quantum theory 5018

81P10

Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) [See also 03G12, 06C15] 2315

81P13

Contextuality in quantum theory 210

81P15

Quantum measurement theory, state operations, state preparations 6254

81P16

Quantum state spaces, operational and probabilistic concepts 784

81P17

Quantum entropies 33

81P18

Quantum state tomography, quantum state discrimination 6

81P20

Stochastic mechanics (including stochastic electrodynamics) 1457

81P40

Quantum coherence, entanglement, quantum correlations 6639

81P42

Entanglement measures, concurrencies, separability criteria 19

81P43

Quantum discord 3

81P45

Quantum information, communication, networks (quantum-theoretic aspects) [See also 94A15, 94A17] 4186

81P47

Quantum channels, fidelity [See also 94A40] 29

81P48

LOCC, teleportation, dense coding, remote state operations, distillation 16

81P50

Quantum state estimation, approximate cloning 525

81P55

Special bases (entangled, mutual unbiased, etc.) 2

81P65

Quantum gates 7

81P68

Quantum computation [See also 68Q09] {For algorithmic aspects, see 68Q12} 8465

81P70

Quantum coding (general) 832

81P73

Computational stability and error-correcting codes for quantum computation and communication processing 9

81P94

Quantum cryptography (quantum-theoretic aspects) [See also 94A60] 1895

81P99

None of the above, but in this section 599

81Qxx

General mathematical topics and methods in quantum theory 30754

81Q05

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 12843

81Q10

Selfadjoint operator theory in quantum theory, including spectral analysis 6305

81Q12

Nonselfadjoint operator theory in quantum theory including creation and destruction operators 534

81Q15

Perturbation theories for operators and differential equations in quantum theory 1669

81Q20

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 3238

81Q30

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40] 1003

81Q35

Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices [See also 81R20] 1129

81Q37

Quantum dots, waveguides, ratchets, etc. [See also 82D20, 82D77] 711

81Q40

Bethe-Salpeter and other integral equations arising in quantum theory 370

81Q50

Quantum chaos [See also 37Dxx] 2036

81Q60

Supersymmetry and quantum mechanics 2020

81Q65

Alternative quantum mechanics (including hidden variables, etc.) 426

81Q70

Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory 1324

81Q80

Special quantum systems, such as solvable systems 555

81Q93

Quantum control 744

81Q99

None of the above, but in this section 1240

81Rxx

Groups and algebras in quantum theory 27237

81R05

Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70] 4470

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] 4369

81R12

Groups and algebras in quantum theory and relations with integrable systems [See also 17Bxx, 37J35] 3313

81R15

Operator algebra methods applied to problems in quantum theory [See also 46Lxx, 81T05] 1592

81R20

Covariant wave equations in quantum theory, relativistic quantum mechanics [See also 81Q35] 925

81R25

Spinor and twistor methods applied to problems in quantum theory [See also 32L25] 1580

81R30

Coherent states [See also 22E45]; squeezed states in quantum theory [See also 81V80] 3172

81R40

Symmetry breaking in quantum theory 3036

81R50

Quantum groups and related algebraic methods applied to problems in quantum theory [See also 16T20, 17B37] 6024

81R60

Noncommutative geometry in quantum theory 1489

81R99

None of the above, but in this section 224

81Sxx

General quantum mechanics and problems of quantization 13424

81S05

Commutation relations and statistics as related to quantum mechanics (general) 2399

81S07

Uncertainty relations, also entropic 18

81S08

Canonical quantization 3

81S10

Geometry and quantization, symplectic methods [See also 53D50] 2460

81S20

Stochastic quantization 364

81S22

Open systems, reduced dynamics, master equations, decoherence [See also 82C31] 1757

81S25

Quantum stochastic calculus 1987

81S30

Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics 1948

81S40

Path integrals in quantum mechanics [See also 58D30, 81Q30, 81T18] 2639

81S99

None of the above, but in this section 634

81Txx

Quantum field theory; related classical field theories [See also 70Sxx] 58014

81T05

Axiomatic quantum field theory; operator algebras 2127

81T08

Constructive quantum field theory 1852

81T10

Model quantum field theories 4296

81T11

Higher spin theories 8

81T12

Effective quantum field theories 18

81T13

Yang-Mills and other gauge theories in quantum field theory [See also 53C07, 58E15] 12537

81T15

Perturbative methods of renormalization applied to problems in quantum field theory 3001

81T16

Nonperturbative methods of renormalization applied to problems in quantum field theory 1139

81T17

Renormalization group methods applied to problems in quantum field theory 2447

81T18

Feynman diagrams 1768

81T20

Quantum field theory on curved space or space-time backgrounds 5786

81T25

Quantum field theory on lattices 2557

81T27

Continuum limits in quantum field theory 492

81T28

Thermal quantum field theory [See also 82B30] 611

81T30

String and superstring theories; other extended objects (e.g., branes) in quantum field theory [See also 83E30] 15576

81T32

Matrix models and tensor models for quantum field theory 15

81T33

Dimensional compactification in quantum field theory 2

81T35

Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) [See also 83E05] 76

81T40

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 9836

81T45

Topological field theories in quantum mechanics [See also 57R56, 58Dxx] 1623

81T50

Anomalies in quantum field theory 1491

81T55

Casimir effect in quantum field theory 409

81T60

Supersymmetric field theories in quantum mechanics 10472

81T70

Quantization in field theory; cohomological methods [See also 58D29] 2133

81T75

Noncommutative geometry methods in quantum field theory [See also 46L85, 46L87, 58B34] 1931

81T99

None of the above, but in this section 1027

81Uxx

Quantum scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40] 8959

81U05

\(2\)-body potential quantum scattering theory {For WKB methods, see also 34E20} 2880

81U10

\(n\)-body potential quantum scattering theory 862

81U15

Exactly and quasi-solvable systems arising in quantum theory 970

81U20

\(S\)-matrix theory, etc. in quantum theory 1537

81U24

Resonances in quantum scattering theory 6

81U26

Tunneling in quantum theory 5

81U30

Dispersion theory, dispersion relations arising in quantum theory 290

81U35

Inelastic and multichannel quantum scattering 688

81U40

Inverse scattering problems in quantum theory 1044

81U90

Particle decays in scattering 12

81U99

None of the above, but in this section 1196

81Vxx

Applications of quantum theory to specific physical systems 33911

81V05

Strong interaction, including quantum chromodynamics 5787

81V10

Electromagnetic interaction; quantum electrodynamics 3918

81V15

Weak interaction in quantum theory 1333

81V17

Gravitational interaction in quantum theory [See also 83Cxx, 83Exx] 2520

81V19

Other fundamental interactions in quantum theory 164

81V22

Unified quantum theories 4307

81V25

Other elementary particle theory in quantum theory 1448

Anyons 6

Nuclear physics 4306

Atomic physics 2791

Molecular physics [See also 92E10] 2587

81V60

Mono-, di- and multipole moments (EM and other), gyromagnetic relations 0

81V65

Quantum dots as quasi particles [See also 82D20] 283

81V70

Many-body theory; quantum Hall effect 4536

81V72

Particle exchange symmetries in quantum theory (general) 9

81V73

Bosonic systems in quantum theory 34

81V74

Fermionic systems in quantum theory 19

81V80

Quantum optics 5320

81V99

None of the above, but in this section 635

Overview

General and overarching topics; collections

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

Number theory

Field theory and polynomials

Commutative algebra

Algebraic geometry

Linear and multilinear algebra; matrix theory

Associative rings and algebras

Nonassociative rings and algebras

Category theory; homological algebra

\(K\)-theory

Group theory and generalizations

Topological groups, Lie groups

Real functions

Measure and integration

Functions of a complex variable

Potential theory

Several complex variables and analytic spaces

Special functions

Ordinary differential equations

Partial differential equations

Dynamical systems and ergodic theory

Difference and functional equations

Sequences, series, summability

Approximations and expansions

Harmonic analysis on Euclidean spaces

Abstract harmonic analysis

Integral transforms, operational calculus

Integral equations

Functional analysis

Operator theory

Calculus of variations and optimal control; optimization

Geometry

Convex and discrete geometry

Differential geometry

General topology

Algebraic topology

Manifolds and cell complexes

Global analysis, analysis on manifolds

Probability theory and stochastic processes

Statistics

Numerical analysis

Computer science

Mechanics of particles and systems

Mechanics of deformable solids

Fluid mechanics

Optics, electromagnetic theory

Classical thermodynamics, heat transfer

Quantum theory

Statistical mechanics, structure of matter

Relativity and gravitational theory

Astronomy and astrophysics

Geophysics

Operations research, mathematical programming

Game theory, economics, finance, and other social and behavioral sciences

Biology and other natural sciences

Systems theory; control

Information and communication theory, circuits

Mathematics education

any	anywhere
cc	classification code
ct	classification text

a & b	logical and	abc*	right wildcard
a \| b	logical or	"ab c"	phrase
!ab	logical not	(ab c)	parentheses

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Mathematics Subject Classification – MSC2020

Overview