Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space

TL;DR

This paper formulates a local D=4 scalar field theory on $ kappa$-deformed Minkowski space as a nonlocal theory on standard Minkowski space, revealing $ kappa$ as a natural regularizer in propagators.

Contribution

It introduces a novel approach to describing $ kappa$-deformed field theories as nonlocal theories on Minkowski space, including explicit interaction vertices.

Findings

$ kappa$ acts as a regularizing parameter in propagators.

The $ kappa$-deformed interaction vertex is explicitly described.

The theory connects nonlocal $ kappa$-deformed fields with standard Minkowski space formulations.

Abstract

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