Dynamical Generation of Solitons in a 1+1 Dimensional Chiral Field Theory: Non-Perturbative Dirac Operator Resolvent Analysis

TL;DR

This paper non-perturbatively analyzes the 1+1 dimensional Nambu-Jona-Lasinio model, revealing stable soliton-like configurations that trap fermions, with explicit profiles and mass calculations, using a reflectionless Dirac operator approach.

Contribution

It introduces a simpler, direct method to analyze saddle points in the model, demonstrating the formation of stable solitons and their properties without relying on inverse scattering techniques.

Findings

Identification of static, space-dependent condensate configurations

Explicit profiles and mass calculations for solitons

Proof that condensates lead to reflectionless Dirac operators

Abstract

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 $\sigx=<\bar\psi\psi>$ and $\pix=<\bar\psii\gam_5\psi>$ 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 $\sigx, \pix$ 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.