Conserved currents and associated symmetries; Goldstone's theorem

Abstract

We consider, in the framework of local field theory with translation symmetry, automorphisms connected with locally conserved currents. We show that such automorphisms lead to symmetries, i.e. are implementable by unitary operators, whenever the smallest mass in the theory is non-zero. Therefore we conclude that a "spontaneously broken symmetry" is possible only in the event that the smallest mass is zero. This establishes the theorem first conjectured by Goldstone. Show more