κ-deformed spin-1/2 field

Abstract

In this paper, we investigate the Poincaré and discrete symmetries of a $κ$-deformed spin-$\tfrac12$ field, extending recent results obtained for scalar fields. We construct an action that is Poincaré invariant and analyze its consequences within the deformed framework. Our results confirm the findings of our recent analysis of the $κ$-deformed scalar field, where we established that there is no action invariant under both Poincaré symmetry and charge conjugation in the $κ$-deformed case, while $\mathcal{CPT}$-symmetry can be restored through a natural deformation of time reversal. Furthermore, we present an explicit calculation of the Noether charges associated with Poincaré symmetry and show that their algebra closes, demonstrating the internal consistency of the theory.