Particle
Statistics| Particle
Statistics |
Identical Particles > s.a. correlations;
Individuality; Leibniz
Principle; Quasiset Theory; representations.
* Idea: In 3+1 or more
dimensions, the wave function for two or more identical particles must be either
symmetric (bosons, satisfying Bose-Einstein statistics)
or antisymmetric (fermions, satisfying Fermi-Dirac statistics)
under particle permutation, 
(–1)2s ;
Exchanging them twice must lead to the same .
@ Conceptual: Sudarshan AJP(75); Dieks Syn(90); Pesic AS(02);
Hilborn & Yuca BJPS(02)
[philosophical]; Milotti
a0705 [Fermi's
views].
@ General references: Tikochinsky & Shalitin AJP(90)
[(anti)symmetrization]; Pesic AJP(91)
[and formulation of quantum mechanics]; Redhead & Teller BJPS(92);
Leinaas & Myrheim
IJMPA(93),
Leinaas ht/96-in
[algebraic]; York qp/00-in;
Ghirardi & Marinatto
FdP(03)qp/02-in,
FdP(04)
[entanglement]; Peshkin PRA(03)qp/02, qp/03 [spin-0];
Huggett qp/02-in
[identity of indiscernibles]; Philippe et al mp/02/JPA
[survey]; French & Rickles qp/03-in;
Goldstein et al JPA(05)qp/04 [all
particles identical]; Niven PLA(05)cm/04
[MB, BE, and FD, combinatorial]; Omar CP(05)qp
[rev]; Saunders SHPMP(06)qp/05
[reason for classical / quantum difference]; Gottesman cm/05 [classical
indistinguishable particles]; Herbut qp/06.
@ And path integrals: Devreese et al FP(01).
@ Conventionality of indistinguishability: Belousek FP(00);
Teller & Redhead
FP(00).
@ Other conceptual: Redhead & Teller FP(91)
[in favor of Fock space aot tensor
product Hilbert
space]; > s.a. particles [existence].
Generalized Statistics > s.a. cosmological
constant; fock
space; information.
* Idea: Statistics
is usually dictated by representations of the permutation group; However,
examples of non-permutation group statistics are known from anyons in 2D and
from Zn, cyclic statistics for
a certain non-gravitational system.
@ General references: Greenberg PRL(90)
[infinite statistics]; Fivel PRL(90);
Chen et al MPLA(96);
Medvedev PRL(97)
[ambiguous statistics]; Greenberg
qp/99;
Polychronakos ht/99-ln
[1D]; Balachandran et al MPLA(01)ht/00 [geons
in 2+1 Chern-Simons theory]; Greenberg ht/00-in
[rev]; Marcinek m.QA/01 [Fock
space]; Surya JMP(04)ht/03 [cyclic
statistics]; Marcinek in(03)m.QA/04 [categorical
approach]; Baez et al ATMP(07)gq/06 [loop
defects in BF theory]; Salvitti CMP(07)
[2D massive Dirac fields]; Greenberg a0804-in
[rev]; Swain a0805 [quantum
gravity effects].
@ Fermions: Niemi & Semenoff PLB(84), PRP(86)
[fractional fermion number];
Arik & Tekin
JPA(02);
Narayana
Swami qp/05 [q-deformed].
Fractional Statistics in 2+1 Dimensions and Anyons > s.a.
Chern-Simons field theories.
* Idea: Objects with
intermediate statistics, arising in some 2D systems, because particle world-lines
may braid;
Wave functions may change
by any real phase under particle exchange; They belong to a 1D representation
of the braid group.
* Features: Fractional
statistics can be exchanged for extra charges/fluxes in 2D; They imply P and T violation;
They do not violate the spin-statistics theorem, because in 2D spin is not
quantized.
* Quons: Elementary excitations
of fields with intermediate statistics, particles characterized by a parameter q which
permits smooth interpolation between Bose
and Fermi statistics; q = 1 gives bosons, q = –1 gives
fermions.
* Simplest type: Semion (phase changes by 
/2;
ground state probably superfluid – superconducting if charged).
* History: Proposed by
F Wilczek in 1982; Applications in the fractal quantum Hall effect and high-Tc superconductivity.
@ I: Khurana PT(89)nov;
Canright & Girvin
Sci(90)mar;
Wilczek PW(91)jan,
SA(91)may.
@ General references: Leinaas & Myrheim NCB(77);
Sorkin PRD(83);
Wu PRL(84);
Wu PRL(84)
[many-body wave functions]; Haldane & Wu PRL(85)
[for vortices in 2D superfluids]; Goldin in(87); Mackenzie & Wilczek
IJMPA(88);
Semenoff PRL(88);
Lavenda & Dunning-Davies
JMP(89);
Wetterich NPB(89);
Imbo et al PLB(90);
Aneziris et al IJMPA(91)
[1D]; Haldane PRL(91);
Hessling & Tscheuschner IJTP(91);
Forte RMP(92);
Gamboa IJMPA(92);
Canright & Johnson JPA(94);
Goldin & Sharp PRL(96);
Tang & Finkelstein ht/96;
Delves et al PRS(97);
Hagen PLB(99)ht [Pauli
term]; Khare 05 [text];
Negro et al JMP(06)mp/05 [formalism];
Lima & Landim EPL(06)ht [fractional
spin].
@ Quons: Goodison & Toms PLA(94)
[canonical partition function]; Greenberg & Hilborn FP(99)ht/98;
Chow & Greenberg
PLA(01)ht/00 [in
relativistic quantum theory]; Jackson & Hogan IJMPD(08)-ht/07 [and
the cosmological constant].
@ Related topics: Müller ZPC(90)
[2D, lattice]; Acharya & Narayana
Swami JPA(94)
[statistical
mechanics], JPA(04)
[and detailed balance]; Isakov et al PLA(96)
[thermodynamics]; Ramanathan PS(99)
[Laughlin
liquids]; Pachos AP(07) [lattice]; > s.a. quantum
computation, quantum
oscillators.
Parastatistics > s.a. Bosonization; path
integrals.
* Idea: They can arise
only if 3 or more particles are present (but in generally covariant theories,
new possibilities arise even with only two particles);
They correspond to higher than 1D representations of the permutation group.
* Para-Fermi: At most p particles
(p 
N)
may occupy a quantum state, antisymmetric; The ordinary case is p =
1.
* Para-Bose: Similar to para-Fermi, but different symmetry under interchange.
@ General references: Green PR(53)
[proposal]; Ohnuki & Kamefuchi 82 [and
quantum field theory]; Meljanac et al MPLA(98)
[as triple operator algebras]; Stoilova & Van
der Jeugt JMP(05), JMP(05)mp [and
Lie (super)algebras]; Maslov TMP(07).
@ Examples: Greenberg PRL(64) [quarks]; Ringwood & Woodward PRL(84)
[monopoles].
@ Related topics: Aneziris et al IJMPA(89), MPLA(89)
[and general covariance]; Govorkov
TMP(94) [non-existence];
Tamura & Ito JMP(07)
[and random point fields].
References > s.a. entanglement;
foundations of quantum mechanics; quantum
technology; spin-statistics; statistical
mechanics.
@ General: Klepikov SPU(87); Bach PLA(90); Dasgupta & Roy PLA(90); Bourdeau & Sorkin
PRD(92); Arnaud et al AJP(99)
[Fermi-Dirac statistics, illustration]; Cahill ht/06 [rotations and statistics].
@ In curved spacetime: Goodison & Toms PRL(93)ht;
Scipioni MPLA(95).
@ On discrete sets: Aneziris IJTP(94); Lulek & Lulek JPA(96) [finite
sets].
@ Other spaces: Ghilardi & Guadagnini NPB(01) [2+1].
@ Fermions and bosons: Rajeev PRD(84)
[F → B]; Paredes & Cirac
cm/02,
et al PRA(02)
[B → F]; Sriramkumar GRG(03)gq/02 [interpolation];
Gough mp/03 [transformation
between Fock spaces]; Pavsic ht/05 [and
Clifford space]; Patton et al PhyA(05)
[thermodynamic equivalence]; > s.a. Bosonization,
Fermionization; dirac
fields [from bosons]; geons and Kinks [fermionic]; spinors
in field theory [from
pure gravity].
@ Tests, experiments: Choubey & Kar PLB(06)
[neutrinos, from supernovas]
@ Related topics: Strominger PRL(93)
[black holes]; MacKenzie et al TMP(94)
[quantum configuration space]; Celeghini et al JPA(95)ht [quantum
field theory]; Brody & Hughston PRS(99)gq/97 [geometrical];
Isakov et al PLB(98)
[observable algebra, 1D]; Oeckl JGP(01)ht/00 [and
quantum groups]; Alexanian & Balachandran PLB(02)ht/01 [geons];
Rajagopal cm/06 [superstatistics].
> Related topics:
see angular
momentum; Configuration
Space; gas; locality [correleations].
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
5 jul 2008