Approximation of quantum chromodynamics at large N

Abstract

In four dimensional chromodynamics the construction of the leading approximation of the l/N expansion encounters considerable difficulties related to the complicated nature of the gluon self-interaction. The authors obtain exact solutions for the quark propagator in the leading l/N approximation of Saynov's model. It is shown that in the case when the bare quark mass is zero two solutions exist, one of them corresponds to spontaneous breaking of the chiral symmetry. Gauge transformations and the spectrum of bound states in this model are discussed.