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 our analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well.Comment: 36 page

Power Series Representations for Bosonic Effective Actions

We develop a power series representation and estimates for an effective action of the form $$\ln\frac{\int e^{f(\phi,\psi)}d\mu(\phi)}{\int e^{f(\phi,0)}d\mu(\phi)}$$ Here, f(φ,ψ) is an analytic function of the real fields φ(x),ψ(x) indexed by x in a finite set X, and d μ(φ) is a compactly supported product measure. Such effective actions occur in the small field region for a renormalization group analysis. The customary way to analyze them is a cluster expansion, possibly preceded by a decoupling expansion. Using methods similar to a polymer expansion, we estimate the power series of the effective action without introducing an artificial decomposition of the underlying space into boxe

Power Series Representations for Complex Bosonic Effective Actions

We develop a power series representation and estimates for an effective action of the form ln e f(φ,ψ) dµ(φ) e f(φ,0) dµ(φ) Here, f(φ, ψ) is an analytic function of the real fields φ(x), ψ(x) indexed by x in a finite set X, and dµ(φ) is a compactly supported product measure. Such effective actions occur in the small field region for a renormalization group analysis. The customary way to analyze them is a cluster expansion, possibly preceded by a decoupling expansion. Using methods similar to a polymer expansion, we estimate the power series of the effective action withou