Degenerate vacuum formalism for spontaneous symmetry breakdown

Abstract

The transformation phi (x) to phi (x)+ alpha of the free massless scalar field are rendered implementable in a separable Hilbert space by adjoining two conjugate operators (belonging to the zero-energy solutions of the wave equation) to the algebra of the usual particle creation and annihilation operators. The result is an alternative formalism for the discussion of spontaneous symmetry breakdown. It is shown that extension of the formalism to the transformations Amu (x) to Amu (x)+ alpha mu of a free massless vector field yields nontrivial zero-energy representations of the Poincare group.