Gauge Generators, Transformations and Identities on a Noncommutative Space

TL;DR

This paper explores gauge transformations and identities on noncommutative spaces, comparing deformed and twisted Leibnitz rules, and computes explicit gauge generator structures, revealing how these relate to commutative space results.

Contribution

It introduces explicit structures of gauge generators in noncommutative spaces and compares deformed and twisted gauge transformations, extending understanding of gauge symmetry in noncommutative geometry.

Findings

Deformed gauge transformations relate to star deformations of commutative results.

Twisted gauge transformations produce a modified mapping consistent with noncommutative structure.

Explicit gauge generator structures are derived for both cases.

Abstract

By abstracting a connection between gauge symmetry and gauge identity on a noncommutative space, we analyse star (deformed) gauge transformations with usual Leibnitz rule as well as undeformed gauge transformations with a twisted Leibnitz rule. Explicit structures of the gauge generators in either case are computed. It is shown that, in the former case, the relation mapping the generator with the gauge identity is a star deformation of the commutative space result. In the latter case, on the other hand, this result gets twisted to yield the desired map.