BRST symmetry of SU(2) Yang-Mills theory in Cho--Faddeev--Niemi decomposition

TL;DR

This paper establishes the nilpotent BRST and anti-BRST symmetries for SU(2) Yang-Mills theory using the Cho--Faddeev-Niemi decomposition, facilitating its quantization and proposing a modified gauge for better reduction.

Contribution

It derives the BRST and anti-BRST transformations for the Cho--Faddeev-Niemi variables, enabling BRST quantization of the decomposed Yang-Mills theory.

Findings

Derived nilpotent BRST and anti-BRST transformations.

Proposed a modified Maximal Abelian gauge.

Facilitated BRST quantization in the decomposed framework.

Abstract

We determine the nilpotent BRST and anti-BRST transformations for the Cho--Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new interpretation given in the previous paper of the Cho--Faddeev-Niemi decomposition. This gives a firm ground for performing the BRST quantization of the Yang--Mills theory written in terms of the Cho--Faddeev-Niemi variables. We propose also a modified version of the new Maximal Abelian gauge which could play an important role in the reduction to the original Yang-Mills theory.