Construction of non-Abelian gauge theories on noncommutative spaces

TL;DR

This paper develops a formalism to construct non-Abelian gauge theories on noncommutative spaces using a star product, enabling explicit action formulation through power series expansion in the noncommutativity parameter.

Contribution

It introduces a systematic method to build non-Abelian gauge theories on noncommutative spaces from a consistency relation, expanding gauge parameters and fields in powers of the noncommutativity parameter.

Findings

Explicit construction of gauge theories on noncommutative spaces

Power series expansion of gauge fields and parameters

Formulation of actions for noncommutative gauge theories

Abstract

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with aconstant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.