Commutator expansion. II. Relativistic reduced Green’s functions and the Lamb shift calculation

Abstract

This is a continuation of an earlier paper [J. Math. Phys. 34, 5509 (1993)]. A projection operator technique is introduced in the Lamb shift calculation in order to manage spurious infrared divergences. The method provides an efficient tool to exhibit factors of the field in the commutator expansion of the Lamb shift. Mass eigenfunction expansion concepts developed elsewhere provide the setting for the new technique. As a by-product of our method, relativistic reduced Green’s functions are found to appear in a natural way. The method may prove useful, since reduced Green’s functions are simpler than the full Green’s functions, and behave like constant operators as regards the parameter integrals.