Ward-Takahashi Identities in Quantum Field Theory with Spontaneously Broken Symmetry

Abstract

For the theory with spontaneously broken phase symmetry, the Ward-Takahashi-type identities, which are qualitatively different from the corresponding ones in the unbroken theory, are proved in framework of quantum field theory. On the other hand, for the spontaneously broken gauge theory, the Ward-Takahashi identities are shown to be the same as those in the unbroken theory, as far as the abelian gauge field is concerned.