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arXiv · 2010.09863

$k$-Minkowski-deformation of $U(1)$ gauge theory

V. G. Kupriyanov·M. Kurkov·P. Vitale
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Abstract

We construct a non-commutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 2008 (2020) 041. We obtain an exact (all orders in the non-commutativity parameter) expression for both the deformed gauge transformations and the deformed field strength, which is covariant under these transformations. The corresponding Yang-Mills Lagrangian is gauge covariant and reproduces the Maxwell Lagrangian in the commutative limit. Gauge invariance of the action functional requires a non-trivial integration measure which, in the commutative limit, does not reduce to the trivial one. We discuss the physical meaning of such a nontrivial commutative limit, relating it to a nontrivial space-time curvature of the undeformed theory. Moreover, we propose a rescaled kappa-Minkowski non-commutative structure, which exhibits a standard flat commutative limit.

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V. G. Kupriyanov, M. Kurkov, P. Vitale. 2020-10-19. $k$-Minkowski-deformation of $U(1)$ gauge theory. https://doi.org/10.1007/jhep01(2021)102

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