The Modified Dirac Equation

TL;DR

This paper explores modifications to the Dirac and Klein-Gordon equations at ultra-relativistic energies, revealing new effects such as the emergence of antiparticles with altered energies when surpassing the Compton wavelength scale.

Contribution

It introduces a modified form of the Dirac equation applicable at ultra-relativistic energies, extending the standard theory to account for new particle effects.

Findings

Modified equations predict antiparticles with slightly different energies

Standard equations valid below the Compton wavelength

New effects emerge at energies beyond the Compton wavelength

Abstract

We consider the behavior of the particles at ultra relativistic energies, for both the Klein-Gordon and Dirac equations. We observe that the usual description is valid for energies such that we are outside the particle's Compton wavelength. For higher energies however, both the Klein-Gordon and Dirac equations get modified and this leads to some new effects for the particles, including the appearance of anti particles with a slightly different energy.