Gauge Theories on quantum Minkowski spaces: $\rho$ versus $\kappa$

Abstract

The $\rho$-Minkowski space-time, a Lie-algebraic deformation of the usual Minkowski space-time is considered. A star-product realization of this quantum space-time together with the characterization of the deformed Poincar\'e symmetry acting on it are presented. It is shown that appearance of UV/IR mixing is expected already in scalar field theories on $\rho$-Minkowski. Classical and one-loop features of a typical gauge theory on this quantum space-time are presented and critically compared to the situation for $\kappa$-Minkowski.