Ward-Takahashi identity

In quantum field theory a Ward-Takahashi identity is nowadays used to designate an identity between correlation functions that follows from symmetries, either global or gauged, of the theory, and which remains valid after renormalization. It was originally used by John Ward and Y. Takahashi to relate the mass renormalization of the electron to its charge renormalization. Later uses include the extension of the proof of Goldstone's theorem to all orders of perturbation in quantum field theory.