Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity

TL;DR

This paper constructs and analyzes scalar field theory on $kappa$-Minkowski space-time, revealing novel symmetry properties, conservation laws, and implications for Doubly Special Relativity.

Contribution

It provides a detailed construction of scalar field actions on $kappa$-Minkowski space-time and explores their symmetry and conservation law modifications.

Findings

Derived the $kappa$-Poincaré algebra co-product from the scalar field action.

Identified six inequivalent energy-momentum conservation laws at four-point interactions.

Connected the modified conservation laws to implications in Doubly Special Relativity.

Abstract

In this paper we recall the construction of scalar field action on $\kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $\Phi^4$ term we investigate the modified conservation laws. We show that the local interactions on $\kappa$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.