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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 760239, 17 pages
http://dx.doi.org/10.5402/2012/760239
Research Article

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

Institute for Experimental and Applied Physics, Christian Albrechts University at Kiel, Leibnizstraße 11, 24118 Kiel, Germany

Received 2 July 2012; Accepted 24 July 2012

Academic Editors: K. Ammari, A. Herrera-Aguilar, D. Ida, and A. Sanyal

Copyright © 2012 Eckart Marsch. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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