Abstract
We construct a gauge theory model on the 4-dimensional ρ-Minkowski space-time, a particular deformation of the Minkowski space-time recently considered. The corresponding star product results from a combination of Weyl quantization map and properties of the convolution algebra of the special Euclidean group. We use noncommutative differential calculi based on twisted derivations together with a twisted notion of noncommutative connection. The twisted derivations pertain to the Hopf algebra of ρ-deformed translations, a Hopf subalgebra of the ρ-deformed Poincaré algebra which can be viewed as defining the quantum symmetries of the ρ-Minkowski space-time. The gauge theory model is left invariant under the action of the ρ-deformed Poincaré algebra. The kinetic part of the action is found to coincide with the one of the usual (commutative) electrodynamics.
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Acknowledgments
JCW thanks P. Bieliavski and P. Martinetti for useful discussions at various stages of this work. He also thanks the Action 21109 CaLISTA “Cartan geometry, Lie, Integrable Systems, quantum group Theories for Applications”, from the European Cooperation in Science and Technology.
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Maris, V., Wallet, JC. Gauge theory on ρ-Minkowski space-time. J. High Energ. Phys. 2024, 119 (2024). https://doi.org/10.1007/JHEP07(2024)119
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DOI: https://doi.org/10.1007/JHEP07(2024)119