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

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) Poincaré 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 Poincaré symmetry and CPT fails in our case. Finally, we discuss the phenomenological consequences of the theory and its possible observational signatures.

41 pages. arXiv admin note: text overlap with arXiv:2009.03135 The published version