Rotational Anomaly and Fractional Spin in the GaugedCP1NonlinearσModel with the Chern-Simons Term

We consider the interacting ${\mathrm{CP}}^1$ nonlinear $\sigma$ 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.