Equivalence of O(3) nonlinear sigma model and the CP1 model: A path integral approach

TL;DR

This paper provides a rigorous proof demonstrating the equivalence between the O(3) nonlinear sigma model and the CP1 model using a path integral approach, clarifying their theoretical relationship.

Contribution

It offers the first rigorous proof of the equivalence between the O(3) nonlinear sigma model and the CP1 model through a path integral method.

Findings

Confirmed the equivalence of the models mathematically

Clarified the theoretical relationship between the models

Provided a rigorous proof using path integrals

Abstract

A rigorous proof is given on the equivalence of the O(3) nonlinear sigma model and the CP1 model via path integral approach.