On The Physical Non-Equivalence of Chiral Bases

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.