  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
$\gamma_\phi$. These divergences cannot be removed by counterterms without
reintroducing redundant operators.
