On the noncommutative fields method in the three-dimensional Yang-Mills theory

TL;DR

This paper explores the application of the noncommutative fields method to three-dimensional non-Abelian gauge theory, revealing how different noncommutativity implementations generate Chern-Simons terms and higher derivative terms.

Contribution

It demonstrates the effects of noncommutative fields on the structure of three-dimensional Yang-Mills theory, specifically the generation of Chern-Simons and higher derivative terms.

Findings

Noncommutativity between canonical momenta generates Chern-Simons term.

Noncommutativity between field operators introduces higher derivative terms.

The method provides insights into the structure of non-Abelian gauge theories.

Abstract

We apply the noncommutative fields method to the three-dimensional non-Abelian gauge theory. We find that, first, implementing the noncommutativity between the canonical momenta implies in generation of the non-Abelian Chern-Simons term, second, if one introduces the noncommutativity between the field operators, the higher derivative terms would arise.