Generalized Goldstone theorem: Automatic imposition of the Higgs mechanismand application to scale and conformal symmetry breaking

Standard discussions of Goldstone's theorem based on a symmetry of the acti on 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 generali zed theorem automatically imposes the Higgs mechanism, i.e., if the expecta tion value of the scalar field is nonzero then the gauge bosons must be mas sive. The other aspect of the Higgs mechanism, the disappearance of the "wo uld be" Goldstone boson, follows directly from the generalized symmetry con dition itself. We also use our generalized Goldstone's theorem to analyze t he case of a system in which scale and conformal symmetries are both sponta neously broken. (C) 2001 American Institute of Physics.