On The Physical Non-Equivalence of Chiral Bases

TL;DR

This paper clarifies misconceptions about the physical significance of chiral phases in Dirac spinor fields, proving that different chiral angles correspond to physically distinct states, thus affirming the importance of chiral bases.

Contribution

It provides a formal proof that chiral angles in Dirac equations lead to physically non-equivalent states, countering prior claims of trivial reducibility.

Findings

Chiral angles define physically distinct particle states.

The Dirac-like equation with arbitrary chiral angles is physically non-equivalent to the standard Dirac equation.

The paper establishes the physical reality of the chiral basis.

Abstract

In this letter we seek to redress lingering misconceptions pertaining to the physicality of the chiral phase of Dirac bi-spinor fields. Demonstrably, the most general first-order partial differential equation for spinor wavefunctions that can be obtained in Minkowski spacetime is the Dirac-like equation which leaves both the mass and chiral angles as free parameters, the so-called Chiral Dirac Equation. Previously, claims have plauged the literature which assert that any attempt to incorporate chirality by such a generalization can be trivially reduced to the case the nominal Dirac Equation. These statements are incorrect. In this letter we present a formal proof demonstrating the physical non-equivalence of particle states whose chiral angles differ, thereby demonstrating unequivocally the physicality of the chiral basis.