Wave Equations on q-Minkowski space

TL;DR

This paper develops a framework for differential calculus on q-Minkowski space, introducing key operators and solving q-analogues of wave equations with plane wave solutions, advancing quantum geometry and field theory.

Contribution

It systematically constructs differential operators on q-Minkowski space and analyzes q-wave equations, providing explicit solutions and gauge analysis for the first time.

Findings

Introduces q-exterior calculus tools like q-Hodge star and q-Laplace-Beltrami operators.

Derives and solves q-d'Alembert and q-Maxwell equations with plane wave solutions.

Analyzes gauge freedom and provides q-spinor formulation of the field tensor.

Abstract

We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing the q-exterior derivative, q-Hodge star operator, q-coderivative, q-Laplace-Beltrami operator and the q-Lie-derivative. With these tools at hand, we then give a detailed exposition of the q-d'Alembert and q-Maxwell equation. For both equations we present a q-momentum-indexed family of plane wave solutions. We also discuss the gauge freedom of the q-Maxwell field and give a q-spinor analysis of the q-field strength tensor.