A NEW LOOK AT GOLDSTONE’S THEOREM

Abstract

The appearance of spontaneously broken symmetries and its bearing on the physical mass spectrum are analyzed in the algebraic setting of local quantum field theory. Within this setting, a generalization of Goldstone’s Theorem is established which does not rely on the existence of conserved currents. Continuous symmetries not satisfying the premises of the theorem can be spontaneously broken even in the presence of a mass gap.