The connection between Dirac dynamic and parity symmetry

TL;DR

This paper explores an alternative method to construct Dirac spinors using Pauli matrices instead of parity, establishing a new connection between Dirac dynamics and parity symmetry.

Contribution

It introduces a novel approach to Dirac spinor construction, emphasizing the role of Pauli matrices over parity in the Lorentz representation interchange.

Findings

Demonstrates an alternative Dirac spinor construction method.

Establishes a new relation between Dirac dynamics and parity symmetry.

Provides insights into the algebraic structure of Dirac spinors.

Abstract

Dirac spinors are important objects in the current literature, the algebraic structure presented in the text-books is a general method to write it, however, not unique. The purpose of the present work is to show an alternative approach to construct Dirac spinors, considering the interchange between the Lorentz representation space (1/2,0) and (0,1/2) made by the "Magic of Pauli matrices" and not by parity, as commonly it was thought. As it is well known, parity operator is related with the Dirac dynamics. The major focus is to establish the relation between Dirac dynamics with parity operator, the reverse path shown in L. D. Speran\c{c}a (2014).