Power Series Representations for Bosonic Effective Actions

We develop a power series representation and estimates for an effective action of the form 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...

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Bibliographic Details
Published inJournal of statistical physics Vol. 134; no. 5-6; pp. 839 - 857
Main Authors Balaban, Tadeusz, Feldman, Joel, Knörrer, Horst, Trubowitz, Eugene
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.03.2009
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Polymer expansion
Renormalization group
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Summary:We develop a power series representation and estimates for an effective action of the form 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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-008-9634-8