Dynamical generation of solitons in a 1 + 1 dimensional chiral field theory: Non-perturbative Dirac operator resolvent analysis

We analyze the 1 + 1 dimensional Nambu-Jona-Lasinio model non-perturbatively. We study non-trivial saddle points of the effective action in which the composite fields σ(x) = 〈ψ̄ψ〉 and π(x) = 〈̄iγ₅ψ〉 form static space dependent configurations. These configurations may be viewed as one dimensional chiral bags that trap the original fermions ("quarks") into stable extended entities ("hadrons"). We provide explicit expressions for the profiles of some of these objects and calculate their masses. Our analysis of these saddle points, and in particular, the proof that the σ(x), π(x) condensations must give rise to a reflectionless Dirac operator, appear to us simpler and more direct than the calculations previously done by Shei, using the inverse scattering method following Dashen, Hasslacher, and Neveu.