Free q-Deformed Relativistic Wave Equations by Representation Theory

TL;DR

This paper derives free q-deformed relativistic wave equations using representation theory, ensuring solutions form irreducible representations of the q-Poincare algebra, and explicitly computes examples like q-Dirac, q-Weyl, and q-Maxwell equations.

Contribution

It uniquely determines q-wave equations from representation theory and explicitly constructs key examples including q-Dirac, q-Weyl, and q-Maxwell equations.

Findings

Derived q-wave equations from irreducible representations

Explicitly computed q-Dirac, q-Weyl, and q-Maxwell equations

Established algebraic structures like q-Clifford algebra

Abstract

In a representation theoretic approach a free q-relativistic wave equation must be such, that the space of solutions is an irreducible representation of the q-Poincare algebra. It is shown how this requirement uniquely determines the q-wave equations. As examples, the q-Dirac equation (including q-gamma matrices which satisfy a q-Clifford algebra), the q-Weyl equations, and the q-Maxwell equations are computed explicitly.