Internal symmetry and the semiclassical method in quantum field theory

Abstract

We apply the methods of Dashen, Hasslacher, and Neveu to quantum field theories with continuous global symmetries. With a U(1) symmetry we show that it is possible to project out a subspace of fixed charge, and to reformulate the theory as one with internal symmetry, but with centrifugal terms arising from rotation in the internal-symmetry space; in the weak-coupling regime, static solutions of this equivalent problem determine the energies of the bound states. Within a particular model in one spatial dimension we demonstrate the existence of such bound states and examine the dependence of their energies upon the charge. The extension of the method to non-Abelian groups is illustrated with SU(2) examples.