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We derive an off-shell recursion relation for correlators that holds at allloop orders. This allows us to prove how generalized amplitudes transform undergeneric field redefinitions, starting from an assumed behavior of theone-particle-irreducible effective action. The form of the recursion relationresembles the operation of raising the rank of a tensor by acting with acovariant derivative. This inspires a geometric interpretation, whose featuresand flaws we investigate.

On Amplitudes and Field Redefinitions