Rotational anomaly and fractional spin in the gauged CP1 nonlinear sigma model with the Chern-Simons term.

Abstract

We consider the interacting ${\mathrm{CP}}^{1}$ nonlinear $\ensuremath{\sigma}$ model in 2 + 1 dimensions in the presence of an Abelian Chern-Simons term and quantize it canonically using the Dirac-Bergmann algorithm. There arises an anomalous term in the angular momentum in presence of the interaction, which in the long-range limit yields the fractional spin for the excitations.