Field redefinitions and infinite field anomalous dimensions

Abstract

Abstract Field redefinitions are commonly used to reduce the number of operators in the Lagrangian by removing redundant operators and transforming to a minimal operator basis. We give a general argument that such field redefinitions, while leaving the S-matrix invariant and consequently finite, lead not only to infinite Green’s functions, but also to infinite field anomalous dimensions γϕ. These divergences cannot be removed by counterterms without reintroducing redundant operators.