Exotic spin and statistics in (2+1)-dimensional canonical quantum field theory

Abstract

Canonical quantization is used to examine the relationship between the addition of a Chern-Simons topological mass term to the action of a (2+1)-dimensional quantum field theory and exotic spin and statistics of elementary quanta. We argue that topologically massive electrodynamics is solved in the long wavelength limit by multi-valued fields with anomalous spin and which create quantum states which have exotic exchange statistics. The quantum states with N particles represent the braid group B N . We examine the implications of our results for the O(3) nonlinear sigma model where the topological current is coupled to topologically massive electrodynamics and the charge carriers are topological solitons.