Non-Abelian Gauge Theory on q-Quantum Spaces

TL;DR

This paper develops non-Abelian gauge theories on q-deformed quantum spaces using covariant derivatives and a Seiberg-Witten map, exemplified by the Manin plane, linking non-commutative and commutative gauge theories.

Contribution

It introduces a method to construct non-Abelian gauge theories on q-deformed spaces via a Seiberg-Witten map, extending gauge theory frameworks to non-commutative geometries.

Findings

Constructed gauge theories on q-deformed spaces using covariant derivatives.

Established a connection between non-Abelian gauge theories on non-commutative and commutative spaces.

Provided an example with the Manin plane illustrating the approach.

Abstract

Gauge theories on q-deformed spaces are constructed using covariant derivatives. For this purpose a ``vielbein'' is introduced, which transforms under gauge transformations. The non-Abelian case is treated by establishing a connection to gauge theories on commutative spaces, i.e. by a Seiberg-Witten map. As an example we consider the Manin plane. Remarks are made concerning the relation between covariant coordinates and covariant derivatives.