The connection between Dirac dynamic and parity symmetry

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).