Dirac Equation and Representation Dependent Scattering Phenomena

TL;DR

This paper reveals that the scattering behavior of Dirac particles, including spin-flip probabilities, depends on the matrix representation used, suggesting hidden physics in relativistic quantum mechanics.

Contribution

It demonstrates that transmission and reflection coefficients in the Dirac equation vary with the chosen Clifford algebra representation, including non-unitary cases leading to quantum interference effects.

Findings

Spin-flip probabilities depend on matrix representation.

Transmission and reflection coefficients vary with representation.

Quantum interference can arise in non-unitary representations.

Abstract

We show that spin-flip probabilities emerge in the relativistic regime for scalar potentials, absent in the standard Dirac representation. We examine 1D scattering for the Dirac equation employing an alternate matrix representation introduced by the Author in an earlier study. We demonstrate that the transmission (T) and reflection (R) coefficients can depend on the chosen representation of the Clifford algebra despite the two representations being related by a unitary or non-unitary transformation. We also show that for the non-unitary case quantum interference may arise in scattering phenomena, a testable experimental signature. This representation dependence hints at hidden physics in how spinor components couple to external steps/barriers, even when the relativistic dispersion relation (E^2=p^2+m^2) is the same.