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.

中文翻译：

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U(1)规范理论的κ-Minkowski-变形

我们按照最近在 JHEP 08 (2020) 041 中提出的一般方法构建了 U(1) 规范理论的非交换 kappa-Minkowski 变形。规范变换和变形场强，在这些变换下是协变的。相应的 Yang-Mills Lagrangian 是规范协变的，并在交换极限中再现了 Maxwell Lagrangian。动作泛函的规范不变性需要一种非平凡的积分测度，在交换极限下，它不会减少到平凡的积分测度。我们讨论了这种非平凡交换极限的物理意义，将其与未变形理论的非平凡时空曲率联系起来。此外，我们提出了一个重新调整的 kappa-Minkowski 非交换结构，