The Exchange Hole in the Dirac Sea

TL;DR

This paper extends the concept of the exchange hole from condensed matter physics to the Dirac sea in quantum electrodynamics, analyzing the internal stability of the electron through a three-fermion correlation framework.

Contribution

It introduces a generalized exchange hole and exchange exciton in QED, providing analytic results for charge and force densities, supported by positronium analogies.

Findings

Analytic expressions for charge densities and force densities of the exchange hole.

Introduction of a three-fermion correlation model for the exchange hole.

Support from positronium negative ion analogies.

Abstract

This work is motivated by the long-standing question about the internal stability of the electron. While one cannot investigate internal properties of a point-like particle, it is fair to analyze the response of the Dirac sea to an electron. For this purpose the concept of an exchange hole is generalized from the Fermi sea of condensed matter physics to the Dirac sea of quantum electrodynamics. In order to conserve charge and angular momentum, an exchange electron is added to the exchange hole, forming a neutral exchange exciton. Consequently, the pair correlation defining the exchange hole is generalized to a three-fermion correlation. An approximation by sequential pair correlations provides analytic results for charge densities, average distances, and force densities of the exchange hole and electron. The analysis is supported by analogies to the negative ion of positronium.