Dirac Equation in $\kappa$-Minkowski space-time

Abstract

In this paper, we derive the Dirac equation in the $\kappa$-deformed Minkowski space-time. We start with $\kappa$-deformed Minkowski space-time and investigate the undeformed $\kappa$-Lorentz transformation valid to all order in the deformation parameter $a$. Using the undeformed $\kappa$-Lorentz algebra, we obtain the $\kappa$-deformed Dirac equation, valid to all order in the deformation parameter $a$. In limit $a\rightarrow$0, we get back the correct commutative result.