The Electromagnetic Properties of Dirac Particles

Abstract

A framework for describing those electromagnetic properties of Dirac (spin-\textonehalf{}) particles which determine their behavior when moving with low momentum through weak, slowly varying, external electromagnetic fields is developed by finding the most general interaction terms which may be added to the Dirac equation for the particle subject to appropriate conditions. The interaction terms found form an infinite series involving arbitrarily high derivatives of the electromagnetic potentials evaluated at the position of the particle. The series of coefficients of these terms then characterize the properties to be described and can be interpreted as a series of moments of the charge and current distribution associated with the Dirac particle. The first coefficient represents the charge of the particle, the second its anomalous magnetic moment. The third is a measure of the spatial extent of the particle's charge distribution, and the corresponding term describes a direct interaction of the particle and the charge distribution responsible for the external electromagnetic field. Higher terms in the series describe direct interactions of the particle with various derivatives of the external charge and current distribution. The correct physical interpretation of the terms is examined by transforming to the Foldy-Wouthuysen (nonrelativistic) representation of the Dirac equation. The consistency of the framework developed with field theoretical results is discussed. Limitations of the characterization derived here and the possibilities of broadening the assumptions on which it is based are examined. The results are applied in the succeeding paper to the interpretation of the electromagnetic properties of nucleons with particular reference to the electron-neutron interaction.