Maps between Deformed and Ordinary Gauge Fields

TL;DR

This paper establishes a correspondence between q-deformed gauge fields and ordinary gauge fields, analyzes q-deformed QED perturbatively, and constructs a star product on a hybrid quantum plane.

Contribution

It introduces a novel map between deformed and ordinary gauge fields and develops a star product on a hybrid quantum plane.

Findings

Perturbative analysis of q-deformed QED at the classical level

Explicit construction of a star product on the hybrid (q,h)-plane

Discussion of gauge fixing via BRST in the deformed setting

Abstract

In this paper, we introduce a map between the q-deformed gauge fields defined on the GL$_{q}(N) $-covariant quantum hyperplane and the ordinary gauge fields. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing $\grave{a} $ la BRST is discussed. An other star product defined on the hybrid $(q,h) $% -plane is explicitly constructed .