$\kappa$-deformed Dirac Equation

TL;DR

This paper develops a $$-deformed Dirac equation in noncommutative spacetime, analyzes its symmetry properties, and investigates its impact on the hydrogen spectrum, providing bounds on the deformation parameter.

Contribution

It introduces a $$-deformed Dirac equation, studies its symmetry violations, and derives experimental bounds on the deformation parameter from hydrogen atom spectra.

Findings

Charge conjugation invariance is broken by $$-deformation.

Parity and time reversal symmetries are preserved.

Bounds on the deformation parameter are close to the Planck length.

Abstract

We construct a Dirac equation in $\kappa$-Minkowski spacetime and analyse its implications. This $\kappa$-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, $a$. We show that the $\kappa$-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the Hydrogen atom spectrum is modified due to the $\kappa$-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter $a$, which are few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle.