Asymmetry in momentum space: restoring ${\cal C}{\cal P}{\cal T}$ invariance of $\kappa$-field theory

TL;DR

This paper investigates the asymmetry between positive and negative energy modes in $ kappa$-field theory within noncommutative spacetime, proposing a deformation of time reversal to restore ${ C}{ P}{ T}$ invariance and analyzing the symmetry properties of the relativistic charges.

Contribution

It introduces a novel approach to restore ${ C}{ P}{ T}$ invariance in $ kappa$-field theory by deforming time reversal symmetry based on the structure of momentum space.

Findings

Charge conjugation and Poincaré invariance are incompatible in this framework.

Deforming time reversal symmetry can restore ${ C}{ P}{ T}$ invariance.

The proposed deformation successfully maintains relativistic charge properties.

Abstract

The positive and negative energy modes of a field theory in $\kappa$-Minkowski/$\kappa$-Poincar\'e noncommutative spacetime have very different symmetry properties. This can be understood geometrically by considering that they span two distinct sectors of a curved momentum space. By performing an explicit direct computation of the relativistic Noether charges and their algebra within the canonical formalism, we identify a striking consequence of this asymmetry in momentum space: charge conjugation and Poincar\'e invariance are incompatible. We then notice how the structure of momentum space suggests that time reversal could be deformed so that the overall ${\cal C}{\cal P}{\cal T}$-invariance is restored. We prove that this new proposal works by studying the transformation properties under deformed discrete symmetries of the new relativistic charges.