On the Majorana Equation: Relations between Its Complex Two-Component and Real Four-Component Eigenfunctions

摘要

We first derive without recourse to the Dirac equation the two-componentMajorana equation with a mass term by a direct linearization of the relativisticdispersion relation of a massive particle. Thereby, we make only use of thecomplex conjugation operator and the Pauli spin matrices, corresponding to theirreducible representation of the Lorentz group. Then we derive the complextwo-component eigenfunctions of the Majorana equation and the related quantumfields in a concise way, by exploiting the so-called chirality conjugationoperator that involves the spin-flip operator. Subsequently, the four-componentspinor solutions of the real Majorana equation are derived, and their intrinsic relationswith the spinors of the complex two-component version of the Majoranaequation are revealed and discussed extensively.