Weyl, Majorana and Dirac Fields from a Unified Perspective

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.

Chirality of Dirac Spinors Revisited

“…Their respective expressions are explicited in function of Pauli matrices in Equations (2)-(4). These sets of gamma matrices are frequently used in the literature (e.g., see [22][23][24][25][26][27][28][29][30]).…”