Maxwell operator on q-Minkowski space and q-hyperboloid algebras

TL;DR

This paper develops a quantum analog of the Maxwell operator on q-Minkowski space algebra, utilizing quantum differential forms and braided tangent vector fields, advancing the mathematical framework of quantum geometry.

Contribution

It introduces a Maxwell operator on q-Minkowski space and constructs quantum differential forms as projective modules, incorporating braided tangent vector fields as q-analogs of Poisson vector fields.

Findings

Defined Maxwell operator on q-Minkowski space algebra

Constructed quantum differential forms as projective modules

Utilized braided tangent vector fields as q-analogs of Poisson vector fields

Abstract

We introduce an analog of the Maxwell operator on a q-Minkowski space algebra (treated as a particular case of the so-called Reflection Equation Algebra) and on certain of its quotients. We treat the space of "quantum differential forms" as a projective module in the spirit of the Serre-Swan approach. Also, we use "braided tangent vector fields" which are q-analogs of Poisson vector fields associated to the Lie bracket sl(2).