Eliminating Electron Self-Repulsion

TL;DR

This paper explores how electron self-repulsion issues in classical and quantum electrodynamics can be addressed, showing that normal-ordering the Coulomb term in the Hamiltonian removes self-repulsion while preserving inter-particle interactions.

Contribution

It demonstrates that fully normal-ordering the Coulomb term in quantum electrodynamics eliminates electron self-repulsion without losing Coulomb interactions.

Findings

Self-repulsion is removed in quantum electrodynamics by normal-ordering.

Normal-ordering preserves Coulomb interactions between distinct particles.

Self-repulsion cannot be eliminated in classical theory without losing Coulomb interactions.

Abstract

Problems of self-interaction arise in both classical and quantum field theories. To understand how such problems are to be addressed in a quantum theory of the Dirac and electromagnetic fields (quantum electrodynamics), we can start by analyzing a classical theory of these fields. In such a classical field theory, the electron has a spread-out distribution of charge that avoids some of the problems of self-interaction facing point charge models. However, there remains the problem that the electron will experience self-repulsion. This self-repulsion cannot be eliminated within classical field theory without also losing Coulomb interactions between distinct particles. But, electron self-repulsion can be eliminated from quantum electrodynamics in the Coulomb gauge by fully normal-ordering the Coulomb term in the Hamiltonian. After normal-ordering, the Coulomb term contains pieces describing attraction and repulsion between distinct particles and also pieces describing particle creation and annihilation, but no pieces describing self-repulsion.