Dirac Equation in the Magueijo-Smolin Approach of Double Special Relativity

TL;DR

This paper explores the Dirac equation within the Magueijo-Smolin framework of Doubly Special Relativity, deriving its forms in momentum and position space to deepen understanding of its semiclassical behavior.

Contribution

It introduces a detailed derivation of the Dirac equation in the Magueijo-Smolin approach, including momentum and position space formulations, based on a deformed dispersion relation.

Findings

Derived the Dirac equation in momentum space.

Formulated the Dirac equation in position space.

Enhanced understanding of semiclassical aspects of the theory.

Abstract

We reconsider in details the Dirac equation in the context of the Magueijo-Smolin approach to the Doubly Special Relativity. Starting from the deformed dispersion relation we obtain the Dirac equation in momentum space, allowing us to achieve a more in-depth study of its semiclassical approach. Finally by means of a deformed correspondence principle we gain access to an equation in the position space.