Application of the Doubly Special Relativity to the Dirac equation formalism

a - Institut de Physique, Equipe ''BioPhyStat'', ICPMB, IF CNRS 2843,
Université Paul Verlaine-Metz, 1 Bd Arago, 57078 Metz, Cedex 3, France
b - Université Mouloud Mammeri, BP 17 Tizi Ouzou, Algérie
c - Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathématiques,
Université de Grenoble I, BP74, 38402 Saint Martin d'Hères, Cedex, France

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 focus on the obtaining of a 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.