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 γ ϕ . These divergences cannot be removed by counterterms without reintroducing redundant operators.

Keywords

• Effective Field Theories
• Renormalization Group