Practical pretheories of QED. II. Choosing the interaction

Abstract

An interaction of the j⋅A form is introduced. The Coester transformation, which connects the Proca and the Coester fields, is extended to the pretheory boson fields when the boson mass counterterms are absent. The Fermi transformation, used to make the Lorentz condition stationary in the weak-convergence limit, is shown to be extendable to the pretheories (sans the freedom of commutator choice, which is usually associated with it). The familiar consequences of including a Fermi transformation (the Heisenberg picture images of the spinor fields do not transform as spinors) are retained, but a suitable limitation on the choice of the spinor charge and mass counterterms will allow the Heisenberg picture forms which are bilinear in the spinor operators to retain their transformation properties. In particular, familiar choices for Lint require that the spinor fields be expressed in the intermediate-Heisenberg picture. The introduction of boson mass counterterms into the practical pretheories is shown to give infinite gauge shifts which are independent of the zero-mass limit. Sufficient conditions for a modified Fermi operator are presented, and an ‘‘obvious’’ candidate is eliminated.