Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry

TL;DR

This paper revisits scalar field theory on $appa$-Minkowski space, analyzing its symmetries, conserved charges, and revealing subtle Lorentz symmetry breaking due to trans-Planckian modes.

Contribution

It provides a detailed analysis of the symmetry structure and conserved charges in $appa$-Minkowski scalar field theory, highlighting subtle Lorentz symmetry breaking effects.

Findings

Presence of an additional trans-Planckian mode

Conserved charge associated with these modes is not Lorentz scalar

Lorentz invariance is subtly broken in the model

Abstract

This paper is devoted to detailed investigations of free scalar field theory on $\kappa$-Minkowski space. After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations. We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.