SOME FUNDAMENTAL BUT ELEMENTARY FACTS ON RENORMALIZATION AND REGULARIZATION: A CRITICAL REVIEW OF THE EIGHTIES

Abstract

The literature of the last ten years is riddled with papers confusing or "even erroneous because their authors forget some facts on regularization and renormalization which should be well-known. We thus propose a short critical review with emphasis on three points: – to every primitive divergence corresponds a normalization condition, i.e. a parameter, even when a minimal scheme is used, – a regularization needs a consistent set of rules, – quantum corrections appear in the Ward identities when a symmetry non-preserving regulator is used, and they have to be compensated for through finite, non-symmetric counterterms. As a corollary, we recall that, being inconsistent, dimensional reduction should be prohibited when one wants to prove general results and, when used in "experimental" calculations, it should come with the necessary warnings.