Free q-Deformed Relativistic Wave Equations by Representation Theory

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.

24 pages, LaTeX; enlarged introduction and conclusion, added references, some minor improvements

References in corpus (7)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
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• The Standard Model on Non-Commutative Space-Time
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Cited by in corpus (10)

• q-Deformed quantum Lie algebras
• Analysis on q-deformed quantum spaces
• q-Exponentials on quantum spaces
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Photonic realization of the kappa-deformed Dirac equation
• Superanalysis on quantum spaces
• Grassmann variables on quantum spaces
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Separation of noncommutative differential calculus on quantum Minkowski space
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems