Spin-Statistics Theorem| 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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