Structure-Independent Electrodynamics in the Electric-Dipole Approximation

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Abstract
We treat the problem of a nonrelativistic charged particle interacting with its own field, by a method originally devised by Kramers. We show that the ambiguities which arise in Kramers' theory vanish when one utilizes a canonical scheme which explicitly deals with the constraints (relations among the dynamical variables) which arise in the course of mass renormalization. To create a consistent canonical theory in the presence of these constraints, it is convenient to introduce new dynamical variables which no longer satisfy the canonical commutation rules. We show that, if one accounts for the constraints, several different renormalized theories are related to each other by canonical transformation, and that each of these theories may be derived from a given unrenormalized theory by a canonical transformation.