Covariant formulation of non-Abelian gauge theories without anticommuting variables

TL;DR

This paper introduces a Lorentz invariant effective action for Yang-Mills theory that depends solely on commuting fields, featuring a bosonic symmetry similar to BRST, offering a new formulation of non-Abelian gauge theories.

Contribution

It presents a novel covariant formulation of non-Abelian gauge theories using only commuting variables, avoiding anticommuting fields.

Findings

Constructed a Lorentz invariant effective action with commuting fields.

Identified a bosonic symmetry analogous to BRST symmetry.

Provides a new perspective on gauge invariance in Yang-Mills theory.

Abstract

A manifestly Lorentz invariant effective action for Yang-Mills theory depending only on commuting fields is constructed. This action posesses a bosonic symmetry, which plays a role analogous to the BRST symmetry in the standard formalism.