κ-Minkowski-deformation of U(1) gauge theory

Abstract

We construct a noncommutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 08 (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 noncommutative structure, which exhibits a standard flat commutative limit.

A preprint version of the article is available at ArXiv.

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Correspondence to V. G. Kupriyanov.

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ArXiv ePrint: 2010.09863

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Kupriyanov, V.G., Kurkov, M. & Vitale, P. κ-Minkowski-deformation of U(1) gauge theory. J. High Energ. Phys. 2021, 102 (2021). https://doi.org/10.1007/JHEP01(2021)102

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Keywords

  • Gauge Symmetry
  • Non-Commutative Geometry