In
mathematics and
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, braid statistics is a generalization of the
spin statistics of
boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spi ...
s and
fermions based on the concept of
braid group
A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing two or more strands of flexible material such as textile yarns, wire, or hair.
The simplest and most common version is a flat, solid, three-strande ...
. While for fermions (Bosons) the corresponding statistics is associated to a phase gain of
(
) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of
under such exchange
or even a non-trivial unitary transformation in the Hilbert space (see
non-Abelian anyons). A similar notion exists using a
loop braid group.
Braid statistics are applicable to theoretical particles such as the two-dimensional
anyons
In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than the two kinds of standard elementary particles, fermions and bosons. In general, the operation of exchangi ...
and their higher-dimensional analogues known as
plektons.
See also
*
Braid symmetry
*
Parastatistics
In quantum mechanics and statistical mechanics, parastatistics is one of several alternatives to the better known particle statistics models (Bose–Einstein statistics, Fermi–Dirac statistics and Maxwell–Boltzmann statistics). Other alt ...
*
Anyon
References
Parastatistics
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