DYNAMICAL GENERATION OF EXTENDED OBJECTS IN A (1-DIMENSIONAL CHIRAL FIELD-THEORY - NONPERTURBATIVE DIRAC OPERATOR RESOLVENT ANALYSIS(1))

We analyze the (1 + 1)-dimensional Nambu-Jona-Lasinio (NJL) model nonp erturbatively. In addition to its simple ground-state saddle points, t he effective action of this model has a rich collection of nontrivial saddle points in which the composite fields sigma(x) = [(psi)over bar> <psi] and pi(x) = [<(psi)over bar>i gamma(5) psi] form static space-de pendent configurations because of nontrivial dynamics. These configura tions may be viewed as one-dimensional chiral ''bags.'' We start our a nalysis of such configurations by asking what kind of initially static {sigma(x), pi(x)} background configurations will remain so under ferm ionic back reaction. By simply looking at the asymptotic spatial behav ior of the expectation value of the fermion number current we show, in dependently of the large N limit, that a necessary condition for this situation to occur is that {sigma(x), pi(x)} give rise to a reflection less Dirac operator. We provide an explicit formula for the diagonal r esolvent of the Dirac operator in a reflectionless {sigma(x), pi(x)} b ackground which produces a prescribed number of bound states. We-analy ze in detail the cases of a single as well as two bound states. We exp licitly check that these reflectionless backgrounds may be tuned such that the large-N saddle-point condition is satisfied. Thus, in the cas e of the NJL model, reflectionlessness is also sufficient to assure th e time independence of the background. In our view, these facts make o ur work conceptually simpler than the previous work of Shei and of Das hen, Hasslacher, and Neveu which were based on the inverse scattering formalism. Our method of finding such nontrivial static configurations may be applied to other (1 + 1)-dim ensional field theories.