1Nexpansion and the theory of composite particles

Abstract

Dynamical structures of nonlinear spinor and bosonic theories are studied in the framework of the $\frac{1}{N}$ expansion. It is shown that a wide class of four-fermion theories contains composite particles and that they can be cast into equivalent field theories with the so-called compositeness condition. With the formation of composite particles, the ultraviolet behavior of a large class of four-fermion theories is improved so that they become renormalizable and well-defined field theories beyond two (but less than four) dimensions in spite of their apparent nonrenormalizability in the conventional perturbation expansions.