Foundations for proper-time relativistic quantum theory

TL;DR

This paper develops a canonical proper-time approach to relativistic quantum theory, introducing three new wave equations that improve agreement with experimental data over the Dirac equation, but still do not fully explain phenomena like the Lamb shift.

Contribution

It introduces a novel canonical proper-time framework for relativistic quantum theory, leading to three new wave equations with positive definite generators.

Findings

New relativistic wave equations with positive definite generators

Improved predictions for Hydrogen spectral data

Inability to fully explain Lamb shift and anomalous magnetic moment

Abstract

This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of relativistic quantum theory, followed by a review of the Dirac equation, providing new insights into the physical properties of both. We then introduce the canonical proper-time theory. For completeness, we give a brief outline of the canonical proper-time approach to electrodynamics and mechanics, and then introduce the canonical proper-time approach to relativistic quantum theory. This theory leads to three new relativistic wave equations. In each case, the canonical generator of proper-time translations is strictly positive definite, so that it represents a particle. We show that the canonical proper-time extension of the Dirac equation for Hydrogen gives results that are consistently closer to the experimental data, when compared to the Dirac equation. However, these results are not sufficient to account for either the Lamb shift or the anomalous magnetic moment.