Relativistic quantum mechanics of the Majorana particle

Abstract

This article is a pedagogical introduction to relativistic quantum mechanics of the free Majorana particle. This relatively simple theory differs from the well-known quantum mechanics of the Dirac particle in several important aspects. First, we present its three equivalent formulations. Next, a so-called axial momentum observable is introduced, and the general solution of the Dirac equation is discussed in terms of eigenfunctions of that operator. We also present pertinent irreducible representations of the Poincaré group. Finally, we show that in the case of massless Majorana particle, the quantum mechanics can be reformulated as a spinorial gauge theory.