The Majorana particles and the Majorana sea

TL;DR

This paper demonstrates how to construct a Majorana fermion field theory starting from a massless Weyl theory by adding a mass term as an interaction, paralleling the Dirac case.

Contribution

It provides a method to derive Majorana field theory from Weyl theory by introducing a mass term as an interaction, extending the approach used for Dirac fields.

Findings

Majorana fields can be constructed from massless Weyl fields with an added interaction.

The procedure parallels the Dirac case, using superpositions of massless fields.

The approach offers a new perspective on the origin of Majorana particles.

Abstract

Can one make a Majorana field theory for fermions starting from the zero mass Weyl theory, then adding a mass term as an interaction? The answer to this question is: yes we can. We can proceed similarly to the case of the Dirac massive field theory. In both cases one can start from the zero mass Weyl theory and then add a mass term as an interacting term of massless particles with a constant (external) field. In both cases the interaction gives rise to a field theory for a free massive fermion field. We present the procedure for the creation of a mass term in the case of the Dirac and the Majorana field and we look for a massive field as a superposition of massless fields.