FRACTIONAL STATISTICS ON COMPACT SURFACES
- 30 April 1991
- journal article
- review article
- Published by World Scientific Pub Co Pte Ltd in Modern Physics Letters B
- Vol. 05 (10) , 675-686
- https://doi.org/10.1142/s0217984991000824
Abstract
General kinematical restrictions on quantum-theories of N identical anyons have been established by using braid groups. For an orientable compact surface (without boundary) of genus g, the statistical parameter θ is a rational multiple of π, θ=πp/v (p and v mutually prime integers), and the number of components of the wavefunction is (a multiple of) vg. The particle-number is N=rv+1−g (r integer) for spinless (S=0) and N=rv for spinning (S=θ/2π) anyons. The restrictions for spinning anyons are consistent with results for fractional quantum Hall systems, nonlinear O(3) field theory, and Chern-Simons theory. The multi-component structure, which appears for g≥1, reflects an internal collective degree of freedom. A comparison with the multi-component wavefunctions needed to describe systems with fractionally charged quasi-particles yields consistency relations between charge and statistics. Non-orientable surfaces do not allow fractional statistics.Keywords
This publication has 0 references indexed in Scilit: