Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces

Abstract

Covariant differential calculi and exterior algebras on quantum homogeneous spaces endowed with the action of inhomogeneous quantum groups are classified. In the case of quantum Minkowski spaces they have the same dimensions as in the classical case. Formal solutions of the corresponding Klein--Gordon and Dirac equations are found. The Fock space construction is sketched.

21 pages, LaTeX file, minor changes

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• Deformed Field Theory on kappa-spacetime
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• Distance Measurement and $\kappa$-Deformed Propagation of Light and Heavy Probes
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Noncommutative Geometry for Pedestrians
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Free q-Deformed Relativistic Wave Equations by Representation Theory
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Spin Representations of the q-Poincare Algebra
• The Dirac operator and gamma matrices for quantum Minkowski spaces
• Quasitriangularity and enveloping algebras for inhomogeneous quantum groups
• T-Minkowski noncommutative spacetimes II: classical field theory
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• Field theoretic models on covariant quantum spaces
• Separation of noncommutative differential calculus on quantum Minkowski space
• Metrics on the Real Quantum Plane