LocalD=4field theory onκ-deformed Minkowski space

2000

We describe the local $D=4$ field theory on $\ensuremath{\kappa}$-deformed Minkowski space as a nonlocal relativistic field theory on standard Minkowski space-time. For simplicity the case of a $\ensuremath{\kappa}$-deformed scalar field $\ensuremath{\varphi}$ with the interaction $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ is considered, and the $\ensuremath{\kappa}$-deformed interaction vertex is described. It appears that the fundamental mass parameter $\ensuremath{\kappa}$ plays the role of regularizing the imaginary Pauli-Villars mass in the $\ensuremath{\kappa}$-deformed propagator.