Collective coordinate quantization of $CP^1$ model coupled to Hopf term revisited

TL;DR

This paper revisits the collective coordinate quantization of the $CP^1$ model coupled to a Hopf term, demonstrating how fractional spin emerges when transitioning between physically inequivalent sectors within the same topological class.

Contribution

It clarifies the conditions under which fractional spin appears in the $CP^1$ model with a Hopf term through collective coordinate quantization.

Findings

Fractional spin arises in specific sectors of the model.

Transitioning between inequivalent sectors reveals new quantum properties.

The approach clarifies the role of topological sectors in quantization.

Abstract

We show that the system where $CP^1$ model coupled to Hopf term can reveal fractional spin in a collective coordinate quantization scheme, provided one makes a transition to physically inequivalent sector within a same solitonic sector characterized by a nonvanishing topological number