The Two-Component Majorana Equation-Novel Derivations and Known Symmetries

Abstract

We revisit the two-component Majorana equation and derive it in a new form by linearizing the relativistic dispersion relation of a massive particle, in a way similar to that used to derive the Dirac equation. We are using thereby the Pauli spin matrices, corresponding to an irreducible representation of the Lorentz group, and a lucid and transparent algebraic approach exploiting the newly introduced spin-flip operator. Thus we can readily build up the Majorana version of the Dirac equation in its chiral representation. The Lorentz-invariant complex conjugation operation involves the spin-flip operator, and its connection to chiral symmetry is discussed. The eigenfunctions of the Majorana equation are calculated in a concise way.