Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces

TL;DR

This paper develops a framework for gauge transformations valued in enveloping algebras for non-abelian gauge groups on non-commutative spaces, enabling finite-component gauge field dynamics via the Seiberg-Witten map.

Contribution

It introduces a method to construct enveloping algebra valued gauge fields and formulates their dynamics on non-commutative spaces using the Seiberg-Witten map.

Findings

Enveloping algebra valued gauge fields can be explicitly constructed.

Finite-component gauge field dynamics are achievable on non-commutative spaces.

The Seiberg-Witten map facilitates this formulation.

Abstract

An enveloping algebra valued gauge field is constructed, its components are functions of the Lie algebra valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.