Chiral Dirac Equation and Its Spacetime and CPT Symmetries

TL;DR

This paper derives a chiral Dirac equation using group theory and projection operators, exploring its fundamental nature and analyzing its spacetime and CPT symmetries to inform physical theory formulation.

Contribution

It introduces a novel derivation of the chiral Dirac equation based on minimal assumptions and examines its symmetry properties, enhancing understanding of fundamental physics.

Findings

Demonstrates the fundamental nature of the chiral Dirac equation.

Analyzes spacetime and CPT symmetries of the derived equation.

Discusses implications for general physical theories.

Abstract

The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincar\'{e} group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption of four linearly independent physical states. We thereby demonstrate the fundamental nature of this form of the Dirac equation. The resulting equation is then examined within the context of spacetime and CPT symmetries with a discussion of the implications for the general formulation of physical theories.