  We derive an off-shell recursion relation for correlators that holds at all
loop orders. This allows us to prove how generalized amplitudes transform under
generic field redefinitions, starting from an assumed behavior of the
one-particle-irreducible effective action. The form of the recursion relation
resembles the operation of raising the rank of a tensor by acting with a
covariant derivative. This inspires a geometric interpretation, whose features
and flaws we investigate.
