Article

Journal of Statistical Physics

, Volume 134, Issue 5, pp 839-857

Power Series Representations for Bosonic Effective Actions

  • Tadeusz BalabanAffiliated withDepartment of Mathematics, Rutgers, The State University of New Jersey
  • , Joel FeldmanAffiliated withDepartment of Mathematics, University of British Columbia
  • , Horst KnörrerAffiliated withMathematik, ETH-Zentrum Email author 
  • , Eugene TrubowitzAffiliated withMathematik, ETH-Zentrum

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Abstract

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 boxes.

Keywords

Polymer expansion Renormalization group