This paper explores the use of a particular collection of perturbation ideas in the computations of the Lamb shift in Q.E.D. (quantum electrodynamics). The stumbling block here is the apparently universal use of renormalization techniques, in the large physical literature on the subject, to handle the divergences arising. Despite the phenomenal numerical success of such computations, guided by amazing physical intuition and insight, there has been right from the start (around the Second World War), a weighty group criticizing these procedures as quite unsatisfactory, this group containing Dirac, Pauli, and others.

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