Spontaneous Breakdown of Symmetry and the Gauge Invariance in a Relativistic Field Theory

Abstract

The Nambu-Jona-Lasinio model in which the helicity current is coupled with a massless chiral gauge field, is discussed in the pair approximation. Our model is invariant under the constant as well as local gauge transformations. We have investigated the excitation spectrum of physical states in this model, under the requirement that the chiral gauge invariance is maintained at every stage. Symmetry breaking solutions are found in a noncovariant form. Contrary to previous assertions, massless fields are still present in our theory. Thus, the physical fields are a massive vector field, a massless vector field and a phase field. It is shown that the gauge transformations are carried by the phase field and the massless vector field, respectively.