$\kappa$-deformed complex fields and discrete symmetries

TL;DR

This paper constructs a $ppa$-deformed complex scalar field theory to analyze how discrete symmetries and CPT invariance are modified by the deformation, revealing a subtle departure from CPT invariance due to different mass-shell constraints for particles and antiparticles.

Contribution

It introduces a $ppa$-deformed scalar field framework that accounts for Lorentz symmetry actions on antiparticles and explores the resulting effects on CPT invariance and discrete symmetries.

Findings

Particles and antiparticles obey different mass-shell constraints.

Deformation leads to a subtle departure from CPT invariance.

Detailed analysis of deformed Poincare9 and discrete symmetries on the complex field.

Abstract

We present a construction of $\kappa$-deformed complex scalar field theory with the objective of shedding light on the way discrete symmetries and CPT invariance are affected by the deformation. Our starting point is the observation that, in order to have an appropriate action of Lorentz symmetries on antiparticle states, these should be described by four-momenta living on the complement of the portion of de Sitter group manifold to which $\kappa$-deformed particle four-momenta belong. Once the equations of motions are properly worked out from the deformed action we obtain that particle and antiparticle are characterized by different mass-shell constraints leading to a subtle form of departure from CPT invariance. The remaining part of our work is dedicated to a detailed description of the action of deformed Poincar\'e and discrete symmetries on the complex field.