Power series representations for complex bosonic effective actions. II. A small field renormalization group flow

Abstract

In a previous paper, we developed a power series representation and estimates for an effective action of the form ln[∫ef(α1,…,αs;z∗,z)dμ(z∗,z)/∫ef(0,…,0;z∗,z)dμ(z∗,z)]. Here, f(α1,…,αs;z∗,z) is an analytic function of the complex fields α1(x),…,αs(x),z∗(x),z(x) indexed by x in a finite set X and dμ(z∗,z) is a compactly supported product measure. Such effective actions occur in the small field region for a renormalization group analysis. We illustrate the technique by a model renormalization group flow motivated by the ultraviolet regime in many boson systems.