Chiral Symmetry Breaking in Quantum Field Theory

Abstract

An analysis of the spontaneous breaking of chiral symmetry in three dimensional electrodynamics is described. It is argued that this model, when treated in a 1/ N expansion, does exhibit spontaneous chiral symmetry breaking. This is established by finding analytic and numer· ical solutions to the Dyson-Schwinger equation and then computing the composite-operator effective potential. During the fifty years since Y uka wa proposed the J[ meson as the intermediary of nuclear forces, our view of this particle has continued to evolve. We now know it to be a quark-antiquark composite, and in quantum chromodynamics, QCD, we have a strong interaction theory that may well describe its dynamics and that of the other hadrons. Among all the hadrons, however, the 1f meson is believed to play a special role. The underlying theory of strong interactions posseses a near chiral symmetry, SU(2h X SU(2) R, because of the approximate masslessness of the up and down quarks. This symmetry must then break spontaneously in order to explain the effective 300 MeV masses that these quarks appear to possess as the constituents of hadrons. The spontaneous breaking of any continuous symmetry necessarily leads to the existence of massless Goldstone bosons, and in the case of chiral symmetry, the 1f mesons approximately play this role. The small bare mass of the up and down quarks leads to a small mass for 1f mesons 1