Chronon corrections to the Dirac equation

TL;DR

This paper introduces a decontracted algebraic model of the Dirac equation, revealing non-locality and a new spin-orbit coupling, with implications for understanding the Standard Model.

Contribution

It proposes a novel algebraic framework for the Dirac equation as a contraction of a simpler non-local theory, offering new insights into fundamental symmetries and interactions.

Findings

Exact Lorentz invariance in the simplified model

Non-locality of about 10^{-25} seconds

Predicted small spin-orbit coupling ~1/N

Abstract

The Dirac equation is not semisimple. We therefore regard it as a contraction of a simpler decontracted theory. The decontracted theory is necessarily purely algebraic and non-local. In one simple model the algebra is a Clifford algebra with 6N generators. The quantum imaginary $\hbar i$ is the contraction of a dynamical variable whose back-reaction provides the Dirac mass. The simplified Dirac equation is exactly Lorentz invariant but its symmetry group is SO(3,3), a decontraction of the Poincare group, and it has a slight but fundamental non-locality beyond that of the usual Dirac equation. On operational grounds the non-locality is ~10^{-25} sec in size and the associated mass is about the Higgs mass. There is a non-standard small but unique spin-orbit coupling ~1/N, whose observation would be some evidence for the simpler theory. All the fields of the Standard Model call for similar non-local simplification.