Eugene Trubowitz

Complex Bosonic Many-Body Models: Overview of the Small Field Parabolic Flow

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many boson system on a three-dimensional lattice at low temperature. It provides an overview of the analysis, given in Balaban et al. (The small field parabolic flow for bosonic many-body models: part 1—main results and algebra, arXiv:1609.01745, 2016, The small field parabolic flow for bosonic many-body models: part 2—fluctuation integral and renormalization, arXiv:1609.01746, 2016), of the ‘small field’ approximation to the ‘parabolic flow’ which exhibits the formation of a ‘Mexican hat’ potential well.

Power series representations for complex bosonic effective actions. I. A small field renormalization group step

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.