Self-consistent β functions in asymptotically free massless field theory

Abstract

In massless field theory with asymptotic freedom a spontaneous mass may be generated through renormalization. This mass is non-analytic in the coupling and via the renormalization group is connected with the usual β function. The development of the β function itself in renormalized perturbation theory provides another connection with the spontaneous mass. In a two-dimensional field theory of four-fermion coupling which is asymptotically free, these connections are exploited to find the infrared behavior of the theory. An argument is made on how the results carry over to all orders of perturbation theory.