A New Route to the Majorana Equation

Abstract

In this paper, we suggest an alternative strategy to derive the complex two-component Majorana equation with a mass term and elucidate the related Lorentz transformation. The Majorana equation is established completely on its own, rather than derived from the chiral Dirac equation. Thereby, use is made of the complex conjugation operator and Pauli spin matrices only. The eigenfunctions of the two-component complex Majorana equation are also calculated. The associated quantum fields are found to describe particles and antiparticles, which have opposite mean helicities and are not their own antiparticles, but correspond to two independent degrees of freedom. The four-component real Dirac equation in its Majorana representation is shown to be the natural outcome of the two-component complex Majorana equation. Both types of equations come in two forms, which correspond to the irreducible left- and right-chiral representations of the Lorentz group.

Keywords

• Majorana field
• chiral symmetry
• Lorentz transformation