Spin-Statistics Theorem

In General > s.a. particle statistics.
* Idea: The statement that integer-spin particles are bosons, half-integer ones fermions.

(Pauli) Exclusion Principle in Quantum Theory
* 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.
* Violation? No compelling reasons to doubt its validity; 2006, Tightest limits come from absence of e transitions to state already occupied by two other electrons, as would be seen in soft X-ray (Cu) fluorescence.
@ General references: Gamow SA(59)jul; Govorkov PLA(89); Broyles qp/99; Massimi BJPS(01) [and Leibniz's Identity of Indiscernibles]; Straumann qp/04-in, Fleming SHPMP(07) [history]; Altunbulak & Klyachko a0802 [and electron density matrix].
@ 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].
@ 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].

In Other Theories
@ Non-commutative: Alavi PS(04)ht/02; Chaichian et al PLB(03) [and CPT]; Alavi PS(04).
@ In curved spacetime: Parker & Wang PRD(89); Guido et al RVMP(01)mp/99; Verch CMP(01)mp [generally covariant].
@ In quantum gravity, geons: Sorkin CMP(88); Dowker & Sorkin CQG(98)gq/96, gq/01-in; Balachandran et al NPB(00)ht/99.
@ Anyons in 3D: Forte IJMPA(92) [path integral approach]; Mund 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), JPA(06) [in cm, conformal field theory]; Boya & Sudarshan IJTP(07)-a0711 [in arbitrary dimensions]; Jackson & Hogan IJMPD(08) [and the cosmological constant].

References > s.a. Dyons; Mapping Class Group; soliton.
@ Reviews: York qp/99, qp/99 [N particles].
@ General: 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]; Berry & Robbins PRS(97) [and geometric phase]; Duck & Sudarshan AJP(98); Hilborn & Tino ed-01; Deck & Walker PS(01); Dobrov JPA(03).
@ Proofs: Kuckert LMP(95)ht/94 [algebraic]; Soloviev TMP(99)ht/06 [including non-local fields]; Massimi & Redhead SHPMP(03) [Weinberg's proof].
@ 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, comment 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).
@ Related topics: Guido & Longo CMP(95) [algebraic]; Fujikawa IJMPA(01)ht [path integral form]; Anastopoulos IJMPA(04)qp/01 [geometric quantization]; Harrison & Robbins mp/03 [group reps]; 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].

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 21 jun 2008