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

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.

18 pages, 2 figures, Comment and two references added

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• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• On the L${}_{\infty }$ structure of Poisson gauge theory
• Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field
• Hamiltonian analysis in Lie-Poisson gauge theory
• Light Propagation in $\kappa$-Minkowski Space-Time: Gauge Ambiguities and Invariance
• T-Minkowski noncommutative spacetimes II: classical field theory
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Nonlocal Lagrangian fields and the second Noether theorem. Non-commutative $U(1)$ gauge theory
• Four-dimensional noncommutative deformations of $U(1)$ gauge theory and $L_{\infty }$ bootstrap