$CP^{1}$ model with Hopf term and fractional spin statistics

TL;DR

This paper revisits the $CP^{1}$ model with the Hopf term using the BFT quantization scheme, and demonstrates fractional spin statistics through semi-classical analysis of topological charge sectors.

Contribution

It introduces the BFT scheme to quantize the $CP^{1}$ model with the Hopf term and explicitly shows fractional spin statistics via semi-classical methods.

Findings

Successful application of BFT scheme to the $CP^{1}$ model with Hopf term

Explicit demonstration of fractional spin statistics in topological sectors

Enhanced understanding of topological charge quantization

Abstract

We reconsider the $CP^{1}$ model with the Hopf term by using the Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of the Dirac quantization method. We also perform a semi-classical quantization of the topological charge Q sector by exploiting the collective coordinates to explicitly show the fractional spin statistics.