Novel perturbative scheme in quantum field theory

Abstract

A novel perturbative technique for solving quantum field theory is proposed. In this paper we explore this scheme in the context of self-interacting scalar field theory. For a ${\phi }^{2p}$ theory the method consists of expanding a ${\phi }^{2(1+\delta )}$ theory in powers of δ. A diagrammatic procedure for computing the terms in this series is given. We believe that for any Green’s function the radius of convergence of this series is finite and is, in fact, 1. Moreover, while the terms in the unrenormalized series are individually divergent, they are considerably less so than in the standard weak-coupling perturbation series. In simple, low-dimensional quantum-field-theory models, the δ expansion gives excellent numerical results. We hope this new technique will ultimately shed some light on the question of whether a (${\phi }^4$ ${)}_4$ theory is free.