Nonlinear $\sigma$-Model in (2+1) dimensions

Abstract

The nonlinear $\sigma$-model in (2+1) dimensions admits topological configurations called skyrmions. The topological charge of skyrmions turn out to be the fermionic number and the fermionic current is dictated by the skyrmion field configuration. The peculiar feature of this model is that a Hopf term introduced into the Lagrangian can lead to exotic spin and fractional statistics.