On the renormalization problem in non-relativistic QED: Formulation of an equivalent renormalization procedure for both non-relativistic and relativistic QED

Abstract

The reasons for the wide-spread incorrect opinion that the non-relativistic QED is a non-renormalizable theory are discussed. It is pointed out that in both non-relativistic and relativistic QED the same energy renormalization condition, which, in the latter case, is reducible to the conventional mass renormalization, holds. Furthermore, by applying the energy renormalization in non-relativistic QED, for the first time, a general energy counter term, leading to finite bound-state Lamb-shift contributions in all orders of the interaction and for any initial radiation field, is derived unambiguously.