  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 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.
