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Symmetry 2013, 5(4), 271-286; doi:10.3390/sym5040271

A New Route to the Majorana Equation

Received: 13 May 2013 / Revised: 30 August 2013 / Accepted: 12 September 2013 / Published: 26 September 2013
Download PDF [289 KB, uploaded 26 September 2013]
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 Majorana field; chiral symmetry; Lorentz transformation
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.

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MDPI and ACS Style

Marsch, E. A New Route to the Majorana Equation. Symmetry 2013, 5, 271-286.

AMA Style

Marsch E. A New Route to the Majorana Equation. Symmetry. 2013; 5(4):271-286.

Chicago/Turabian Style

Marsch, Eckart. 2013. "A New Route to the Majorana Equation." Symmetry 5, no. 4: 271-286.

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