Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics

Abstract

We consider gauge theories on Poisson manifolds emerging as semiclassical approximations of noncommutative spacetime with Lie algebra type noncommutativity. We prove an important identity, which allows to obtain simple and manifestly gauge-covariant expressions for the Euler-Lagrange equations of motion, the Bianchi and the Noether identities. We discuss the non-Lagrangian equations of motion, and apply our findings to the $\kappa$-Minkowski case. We construct a family of exact solutions of the deformed Maxwell equations in the vacuum. In the classical limit, these solutions recover plane waves with left-handed and right-handed circular polarization, being classical counterparts of photons. The deformed dispersion relation appears to be nontrivial.

Revised version; published in JHEP; 24 pages

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Cited by in corpus (4)

• On Poisson Electrodynamics With Charged Fields
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Hamiltonian analysis in Lie-Poisson gauge theory
• Light Propagation in $\kappa$-Minkowski Space-Time: Gauge Ambiguities and Invariance