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We analyze the 1+1 dimensional Nambu-Jona-Lasinio model non-perturbatively.We study non-trivial saddle points of the effective action in which thecomposite fields $\sigx=<\bar\psi\psi>$ and $\pix=<\bar\psii\gam_5\psi>$ formstatic space dependent configurations. These configurations may be viewed asone dimensional chiral bags that trap the original fermions (``quarks'') intostable extended entities (``hadrons''). We provide explicit expressions for theprofiles of some of these objects and calculate their masses. Our analysis ofthese saddle points, and in particular, the proof that the $\sigx, \pix$condensations must give rise to a reflectionless Dirac operator, appear to ussimpler and more direct than the calculations previously done by Shei, usingthe inverse scattering method following Dashen, Hasslacher, and Neveu.Comment: 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 correction

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