  Standard discussions of Goldstone's theorem based on a symmetry of the action
assume constant fields and global transformations, i.e., transformations which
are independent of spacetime coordinates. By allowing for arbitrary field
distributions in a general representation of the symmetry we derive a
generalization of the standard Goldstone's theorem. When applied to gauge
bosons coupled to scalars with a spontaneously broken symmetry the generalized
theorem automatically imposes the Higgs mechanism, i.e. the gauge bosons become
massive. The other aspect of the Higgs mechanism, the disappearance of the
would-be Goldstone boson, follows directly from the generalized symmetry
condition itself. We also use our generalized Goldstone's theorem to analyze
the case of a system in which scale and conformal symmetries are both
spontaneously broken.
