Diffeomorphisms of scalar quantum fields via generating functions

Abstract

We study the application of formal diffeomorphisms to scalar fields. We give a new proof that interacting tree amplitudes vanish in the resulting theories. Our proof is directly at the diagrammatic level, not appealing to the path integral, and proceeds via a generating function analysis, so it is more insightful than previous proofs. Along the way, we give new combinatorial proofs of some Bell polynomial identities, and we comment on the connection with the combinatorial Legendre transform.