$\kappa$-deformed complex scalar field: conserved charges, symmetries and their impact on physical observables

TL;DR

This paper analyzes a $$-deformed complex scalar field model, revealing conserved charges forming Poincare9 algebra, relativistic invariance, subtle CPT violation, and discussing potential observational implications.

Contribution

It demonstrates that the $$-deformed scalar field maintains Poincare9 symmetry with conserved charges, but exhibits non-standard boosts and CPT violation, expanding understanding of deformed quantum field theories.

Findings

The model has ten conserved Noether charges forming Poincare9 algebra.

Relativistic invariance is preserved despite non-local boost representations.

The theory subtly violates CPT symmetry while maintaining equal particle and antiparticle masses.

Abstract

In this paper we revisit the model of $\kappa$-deformed complex scalar field. We find that this model possesses ten conserved Noether charges that form, under commutators, a representation of (undeformed) Poincar\'e algebra. It follows that the theory is relativistic and does not break Lorentz invariance. However the spacetime representation of boosts is not standard, and contains a non-local translation, different for positive and negative energy modes. It then follows that although the masses of particles and anti-particles are equal, the theory violates CPT symmetry in a subtle way. We explain why the Jost-Wightman-Greenberg theorem of equivalence of the Poincar\'e symmetry and CPT fails in our case. Finally, we discuss the phenomenological consequences of the theory and its possible observational signatures.