THE LAX PAIR OF A GENERALIZED THIRRING MODEL

Abstract

The system of coupled nonlinear partial differential equations called the Massive Thirring Model is reviewed. In particular it is analyzed in the chiral fermion version, which is extended by introducing a local gauge symmetry in place of the usual global symmetry. This is done by minimally coupling the fermions with a SU L(2) ⊗ SU R(2) gauge potential. Following the formalism of path integrals, we then formulate the study of chiral gauge anomalies in the quantum theory of this gauge extended model. The ultimate goal of it would be to compute the divergence of the chiral fermion current for a nonlinear anomalous theory. Actually, in this work we merely exhibit the Lax pair representation of the system of partial differential equations just derived; it holds to the first order approximation in the infinitesimal gauge parameters and coupling constants present. Our aim is to hint a motivation in searching for explicit solutions of anomalous nonlinear gauge field theories, at least in simple cases.