A new Map between Quantum Gauge Theories defined on a Quantum hyperplane and ordinary Gauge Theories: q-deformed QED

TL;DR

This paper introduces a novel mapping between q-deformed gauge theories on quantum hyperplanes and ordinary gauge theories, exemplified through a perturbative analysis of q-deformed QED, extending the Seiberg-Witten map concept.

Contribution

It presents a new explicit map connecting q-deformed gauge theories on quantum hyperplanes with standard gauge theories, broadening the understanding of quantum deformations in gauge theories.

Findings

Established a classical perturbative framework for q-deformed QED.

Analyzed gauge fixing procedures using BRST formalism.

Demonstrated the analogy with the Seiberg-Witten map.

Abstract

We introduce a new map between a q-deformed gauge theory on a general GL_{q}(N)-covariant quantum hyperplane and an ordinary gauge theory in a full analogy with Seiberg-Witten map. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing a la BRST is discussed