Spin-Statistics Theorem  

In General > s.a. Dyons; Mapping Class Group; particle statistics; soliton.
* Idea: The statement that integer-spin particles are bosons (obey Bose-Einstein statistics), while half-integer ones fermions (obey Fermi-Dirac statistics); In Weinberg's proof, one sees that causality, Poincaré invariance, positive energies and positive probability imply the spin-statistics relation.
@ Reviews: York qp/99, qp/99 [N particles].
@ General references: Fierz HPA(39)-a1704; Pauli PR(40); Lüders & Zumino PR(58); Arnowitt & Deser JMP(62); Streater & Wightman 64; Finkelstein & Rubinstein JMP(68); Tscheuschner IJTP(89); Balachandran et al MPLA(90), IJMPA(93); Forte & Jolicoeur NPB(91) [2+1 dimensions]; Duck & Sudarshan AJP(98)apr, 98; Hilborn & Tino ed-01; Deck & Walker PS(01); Dobrov JPA(03); Reyes-Lega & Papadopoulos FP(10)-a0910 [Berry-Robbins approach]; Marchetti FP(10) [spin-statistics transmutation]; Papadopoulos & Reyes-Lega FP(10) [Berry-Robbins approach, geometric]; Suoranta a1008-wd [generalized]; Lian a1208 [SU(2) × C × T as intrinsic reason]; Curceanu et al AJP(12)jul [RL]; Bennett FP(15)-a1504 [in relativistic quantum mechanics]; Unnikrishnan a1906 [the physics].
@ Proofs: Kuckert LMP(95)ht/94 [algebraic]; Soloviev TMP(99)ht/06 [including non-local fields]; Massimi & Redhead SHPMP(03) [Weinberg's proof]; Doplicher FP(10)-a0907-conf [from local observable quantities and first principles]; Reyes-Lega & Benavides FP(10)-a0911 [configuration-space approach]; Santamato & De Martini a1604 [based on symmetry group considerations].
@ And geometric phase: Berry & Robbins PRS(97); Bandyopadhyay PRS(10).
@ And locality: Greenberg PLB(98)ht/97; O'Hara qp/01.
@ In non-relativistic theory: Peshkin PRA(03)qp/02; Allen & Mondragon qp/03 [absence, ?]; Shaji & Sudarshan qp/03, comments Puccini & Vucetich qp/04, S&S qp/04, P&V qp/05; Kuckert PLA(04)qp/02 [2D and 3D], & Mund AdP(05)qp/04; Hagen PRA(04) [no connection in Galilean field theory]; Peshkin qp/04, FP(06); Jabs FP(10)-a0810.
@ Related topics: Guido & Longo CMP(95) [algebraic]; Fujikawa IJMPA(01)ht [path-integral form]; Anastopoulos IJMPA(04)qp/01 [geometric quantization]; Harrison & Robbins JMP(04)mp/03 [group representations]; O'Hara FP(03)qp [and rotations]; da Cruz ht/04 [spin, Hausdorff dimension and writhing number of quantum paths]; Unnikrishnan gq/04 [and gravity]; Gilra a0909, Good IJMPA(13)-a1205 [from the dynamics?]; Santamato & De Martini a1408 [and intrinsic helicity, in Conformal Quantum Geometrodynamics].
> Online resources: see John Baez's page; Wikipedia page.

(Pauli) Exclusion Principle in Quantum Theory > s.a. crystals [Pauli crystals].
* Idea, in quantum mechanics: Two fermions cannot occupy the same state, because if they did, the wave function would be both symmetric and antisymmetric under exchange of the two particles.
* Idea, in quantum field theory: It is encoded in the commutation relations of creation and annihilation operators; The only possible modifications to the boson/fermion commutation relations are the ones leading to parastatistics.
* Consequences: It explains the properties of atoms, their classification in the periodic table, and features of complex molecules, and is responsible for the stability of matter.
* Violation? There are no compelling reasons to doubt its validity; 2006, The tightest limits come from the absence of electron transitions to states already occupied by two other electrons, as would be seen in soft X-ray (Cu) fluorescence; 2015, The VIP (Violation of the Pauli exclusion principle) experiment established a limit on the probability that the exclusion principle is violated by electrons (searching for forbidden atomic transitions in copper), and was recently upgraded.
@ General references: Pauli ZP(25); Gamow SA(59)jul; Govorkov PLA(89); Broyles qp/99; Massimi BJPS(01) [and Leibniz's Identity of Indiscernibles]; Straumann qp/04-conf, Fleming SHPMP(07) [history]; Altunbulak & Klyachko CMP(08)-a0802, Klyachko a0904/PRL [and electron density matrix]; García-Calderón & Mendoza-Luna PRA(11)-a1104 [effect on decays]; Kaplan FP(13), a1902 [rev].
@ Violation? Greenberg & Mohapatra PRL(89) [later retracted]; Dolgov & Smirnov PLB(05)hp [for neutrinos, and astrophysics]; Ignatiev & Kuzmin PLA(06) [for neutrinos, and non-standard commutation relations]; Jackson PRD(08)-a0809 [in superstring theory]; Addazi & Bernabei a1901 [non-commutative gravity, tests].
@ Experiment: Sudbery Nat(90)nov, Kekez et al Nat(90)nov [upper limit to violation]; Ramberg & Snow PLB(90); Novikov et al PLB(90); VIP collaboration PLB(06)qp [electrons]; Barabash FP(10) [rev]; Bartalucci et al FP(10), Curceanu et al FP(11) [VIP results]; Bernabei et al FP(10) [nuclear processes, in NaI(Tl) scintillators]; Piscicchia et al APPB(15)-a1501 [VIP results]; Marton et al JPCS(15)-a1503 [high-sensitivity tests]; Addazi et al ChPC(18)-a1712 [proposed underground experiments, and tests of non-commutative spacetime]; Shi et al EPJC(18)-a1804 [search for violation]; Marton et al JPCS(19)-a1903 [high sensitivity].
@ Generalized Pauli constraints: Eisert Phy(13), viewpoint on Schilling et al PRL(13); Schilling PhD(14)-a1507.

Spin-Statistics Theorem in Other Theories
@ Non-commutative: Alavi PS(04)ht/02; Chaichian et al PLB(03) [and CPT]; Alavi PS(04); Srivastava PhD-a1309 [in the Groenewold-Moyal plane].
@ In curved spacetime: Parker & Wang PRD(89); Guido et al RVMP(01)mp/99; Verch CMP(01)mp [generally covariant]; Fewster a1503-proc, IJMPD(16)-a1603-MG14 [in locally covariant quantum field theory].
@ In quantum gravity, geons: Sorkin CMP(88); Dowker & Sorkin CQG(98)gq/96, gq/01-proc; Balachandran et al NPB(00)ht/99.
@ Anyons in 3D: Forte IJMPA(92) [path-integral approach]; Mund CMP(09)-a0801 [and plektons]; > s.a. particle statistics.
@ Related topics: Anandan PLA(98)ht [and Kaluza-Klein theory]; Finkelstein LMP(00) [q-Lorentz group]; Morgan AJP(04)nov, JPA(06) [in classical mechanics and conformal field theory]; Boya & Sudarshan IJTP(07)-a0711 [in arbitrary dimensions]; Jackson & Hogan IJMPD(08) [and the cosmological constant]; Johnson-Freyd AGT(17)-a1507 [functorial setting, topological version]; > s.a. types of quantum field theories [higher-spin].

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