Spontaneously broken gauge symmetries. IV. General gauge formulation

The advent of the dimensional-regularization procedure allows the study of renormalizability of spontaneously broken gauge theories formulated in a wide class of gauges. We derive and study the Ward-Takahashi identities appropriate to such gauges. A consequence of the Ward-Takahashi identities is that the physical S matrix is invariant under a variation of the gauge condition. As remarked before, since the variation of a parameter in the $R_{\xi }$-gauge formulation shifts the masses of unphysical excitations, the above result, the $\xi$ independence of the physical S matrix, implies that the unphysical excitations cannot contribute to the sum over intermediate states, establishing the unitarity of the S matrix. We also give the renormalization procedure of a model formulated in the $R_{\xi }$ gauge.