Star product and interacting fields on $\kappa$-Minkowski space

TL;DR

This paper derives the explicit form of the scalar field interaction term on $$-Minkowski space using star products, and investigates the impact on conservation laws and threshold anomalies, finding no anomalies at leading order.

Contribution

It extends previous methods to explicitly formulate the $$-Minkowski star product and analyzes its effects on interaction terms and conservation rules.

Findings

Explicit $$-Minkowski star product derived.

Interaction terms do not produce threshold anomalies at leading order.

Conservation rules are deformed but consistent with no anomalies.

Abstract

In this note we extend the methods developed by Freidel et al. [arXiv:hep-th/0612170] to derive the form of $\phi^4$ interaction term in the case of scalar field theory on $\kappa$-Minkowski space, defined in terms of star product. We present explicit expressions for the $\kappa$-Minkowski star product. Having obtained the the interaction term we use the resulting deformed conservation rules to investigate if they lead to any threshold anomaly, and we find that in the leading order they do not, as expected.