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 κ-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.
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Acknowledgments
M.K. and P.V. acknowledge partial financial support from INFN through Iniziativa Specifica GEOSYM-QFT. The research of P.V. was carried out in the frame of Programme STAR Plus, financially supported by UniNA and Compagnia di San Paolo. V.G.K. acknowledges support from the CNPq Grant 304130/2021-4 and the FAPESP Grant 2021/09313-8.
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Kupriyanov, V.G., Kurkov, M.A. & Vitale, P. Lie-Poisson gauge theories and κ-Minkowski electrodynamics. J. High Energ. Phys. 2023, 200 (2023). https://doi.org/10.1007/JHEP11(2023)200
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DOI: https://doi.org/10.1007/JHEP11(2023)200