Quantum causality constraints on kappa-Minkowski space-time

Abstract

The κ-Minkoswki space-time provides a (quantum) noncommutative deformation of the usual Minkowski space-time. However, a notion of causality is difficult to be defined in such a space with noncommutative time. In this paper, we define a notion of causality on a (1 + 1)-dimensional κ-Minkoswki space-time using the more general framework of Lorentzian noncommutative geometry. We show that this notion allows specific causal relations, but limited by a general constraint which is a quantum generalization of the traditional speed of light limit.