Weyl, Majorana and Dirac fields from a unified perspective

TL;DR

This paper provides a unified, representation-theoretic derivation of Weyl, Majorana, and Dirac fields, emphasizing fundamental aspects often omitted in introductory relativistic fermion theory courses.

Contribution

It offers a self-contained, Lorentz group-based formalism for fermionic fields without relying on Lagrangian methods, filling a gap in standard educational approaches.

Findings

Unified derivation of fermionic fields from Lorentz representations

Clarification of fundamental aspects of relativistic fermion theory

Exclusion of Lagrangian methods in the formalism

Abstract

A self-contained derivation of the formalism describing Weyl, Majorana and Dirac fields from a unified perspective is given based on a concise description of the representation theory of the proper orthochronous Lorentz group. Lagrangian methods play no role in the present exposition, which covers several fundamental aspects of relativistic field theory which are commonly not included in introductory courses when treating fermionic fields via the Dirac equation in the first place.