Self-interacting quantum electron

TL;DR

This paper proposes a self-interacting quantum model of the electron using a non-local Dirac framework, revealing dynamics through projective operator representations and exploring wave solutions with dispersion laws similar to de Broglie’s.

Contribution

It introduces a novel self-interacting quantum electron model based on non-local Dirac equations and analyzes its wave solutions and dispersion relations.

Findings

Travel-wave solutions of the field equations were found.

The dispersion law asymptotically matches de Broglie’s law.

Energy-momentum dynamics are described by quasi-linear PDEs.

Abstract

A model of self-interacting quantum non-local Dirac's electron has been proposed. Its dynamics was revealed by the projective representation of operators corresponding to spin/charge degrees of freedom. Energy-momentum field is described by the system of quasi-linear "field-shell" PDE's following from the conservation law expressed by the affine parallel transport of the energy momentum vector field in CP(3). I discuss here travel-wave solutions of these equations and the "off-shell" dispersion law asymptotically coinciding with the "on-shell" de Broglie dispersion law.