nLab
braid group statistics

Idea

In quantum physics one speaks of the “statistics” of a particle species or other object when referring to the irreducible representation of the group which exchanges identical such particles that it belongs to. Typically this is the symmetric group and accordingly one speaks of boson and fermion statistics. But in special cases, namely whenever the codimension in space of the objects in question is 1 (e.g. point particles in 2-dimensional quantum field theories), accordingly in this situation these may have what is then called braid group statistics and one speaks of anyons.

Related concepts

• boson, fermion, anyon

• parastatistics

References

• Klaus Fredenhagen, Karl-Henning Rehren, Bert Schroer, Superselection sectors with braid group statistics and exchange algebras

  I: General theory (Euclid)

  II: Geometric aspects and conformal covariance (pdf)

• Jürg Fröhlich, F. Gabbiani, Braid statistics in local quantum theory, Reviews in Mathematical Physics, Volume 2, Issue 03, pp. 251-353 (1990).

Discussion of braid group statistics of string-localized quantum fields or similar 1-dimensional entities in dimension 2+1 was maybe first discussed in

• J. M. Leinaas and J. Myrheim, On the Theory of Identical Particles, Il Nuovo Cimento 37 b (1977), 1-23.