\kappa-deformed spin-1/2 field

TL;DR

This paper develops a Poincaré invariant action for a $$-deformed spin-1/2 field, extending previous work on scalar fields, and confirms the algebraic consistency of the deformed symmetry charges.

Contribution

It constructs a consistent $$-deformed spin-1/2 field theory with explicit symmetry charges and analyzes its invariance properties.

Findings

Constructed a Poincare9 invariant action for the $$-deformed spin-1/2 field.

Calculated and verified the closure of the Noether charge algebra.

Confirmed the absence of simultaneous invariance under Poincare9 and charge conjugation in the deformed setting.

Abstract

In this paper, we investigate the $\kappa$-deformed theory of a spin-1/2 field. We construct an action that is Poincar\'e invariant and analyze its consequences within the deformed framework. Our results confirm the findings of our recent analysis of the $\kappa$-deformed scalar field, where we established that there is no action invariant under both Poincar\'e symmetry and charge conjugation in the $\kappa$-deformed case. Furthermore, we present an explicit calculation of the Noether charges associated with Poincar\'e symmetry and show that their algebra closes, demonstrating the internal consistency of the theory.