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arXiv · 2201.10191

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

Andrea Bevilacqua·Jerzy Kowalski-Glikman·Wojciech Wislicki
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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.

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Andrea Bevilacqua, Jerzy Kowalski-Glikman, Wojciech Wislicki. 2022-01-25. $\kappa$-deformed complex scalar field: conserved charges, symmetries and their impact on physical observables. https://doi.org/10.1103/physrevd.105.105004

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