INFRARED BEHAVIOR OF SYSTEMS WITH GOLDSTONE BOSONS

Abstract

We develop various complementary concepts and techniques for handling quantum fluctuations of Goldstone bosons. We emphasize that one of the consequences of the masslessness of Goldstone bosons is that the longitudinal fluctuations also have a diverging susceptibility characterized by an anomalous dimension (d-2) in space–time dimensions 2<d<4. In d=4 these fluctuations diverge logarithmically in the infrared region. We show the generality of this phenomenon on the basis of (i) Renormalization group flows, (ii) Ward identities, and (iii) Schwinger–Dyson equations. We also obtain an explicit form for the generating functional of one-particle irreducible vertices of the O(N) (non)linear σ models in the leading 1/N approximation. We show that this incorporates all infrared behavior correctly both in linear and nonlinear σ models. Some consequences are discussed briefly.