English

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

High Energy Physics - Theory 2011-04-15 v2

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=<ψˉψ>\sigx=<\bar\psi\psi> and \pix=<\psiiˉ\gam5ψ>\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\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.

Keywords

Cite

@article{arxiv.hep-th/9610054,
  title  = {Dynamical Generation of Solitons in a 1+1 Dimensional Chiral Field Theory: Non-Perturbative Dirac Operator Resolvent Analysis},
  author = {J. Feinberg and A. Zee},
  journal= {arXiv preprint arXiv:hep-th/9610054},
  year   = {2011}
}

Comments

10 pages, 2 figures, LaTex. Talk delivered by J.Feinberg at the Workshop on Low Dimensional Field Theory at Telluride, CO (August 1996). To appear in the conference proceedings. Minor typographical corrections