Introduction

Abstract

The Dirac equation plays a fundamental role in relativistic quantum mechanics and in quantum field theory. It describes spin 1/2 particles, including electrons, neutrinos, muons, protons, neutrons, quarks, and their corresponding anti-particles. The Dirac equation has been extremely successful, even in its one-particle interpretation, in calculating the relativistic hydrogen atom spectrum, the $g_{s}$-factor of the electron’s magnetic moment [1], and the spin-orbit coupling for the electron. It has also been used to calculate the Coulomb scattering amplitude [2] and even to obtain meaningful results in its ultra-relativistic limit, where the mass $m\rightarrow 0$ [3]. In fact a vast and rather recent research area has arisen, where the ($2+1$) ultra-relativistic $(m=0)$ Dirac equation is used to describe curved graphene and semi-metals [4].