An Explicit Large Versus Small Field Multiscale Cluster Expansion

DOI10.1142/S0129055X97000063zbMath0870.60100arXivhep-th/9605094OpenAlexW2044033044MaRDI QIDQ3130093

Abdelmalek Abdesselam, Vincent Rivasseau

Publication date: 22 April 1997

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9605094

zbMATH Keywords

Yang-Mills theorySchwinger functionscluster expansionrenormalization group techniques

Mathematics Subject Classification ID

Other physical applications of random processes (60K40) Renormalization group methods applied to problems in quantum field theory (81T17) Renormalization group methods in equilibrium statistical mechanics (82B28)

Related Items (14)

Clustering bounds on \(n\)-point correlations for unbounded spin systems ⋮ Constructive field theory in zero dimension ⋮ A second-quantized Kolmogorov-Chentsov theorem via the operator product expansion ⋮ Tree quantum field theory ⋮ The weakly dependent strong law of large numbers revisited ⋮ From constructive field theory to fractional stochastic calculus. II: Constructive proof of convergence for the Lévy area of fractional Brownian motion with Hurst index \(\alpha \in \left(\frac{1}{8},\frac{1}{4}\right)\) ⋮ Constructive field theory and applications: Perspectives and open problems ⋮ Unnamed Item ⋮ A complete renormalization group trajectory between two fixed points ⋮ Generalized constructive tree weights ⋮ Inductive approach to loop vertex expansion ⋮ The fundamental theorem of calculus for a matroid ⋮ Single scale cluster expansions with applications to many Boson and unbounded spin systems ⋮ Approximating sums by integrals only: multiple sums and sums over lattice polytopes

Cites Work

• Convergent perturbation expansions for Euclidean quantum field theory
• Grad \(\phi\) perturbations of massless Gaussian fields
• Construction of \(Y M_ 4\) with an infrared cutoff
• Large-field versus small-field expansions and Sobolev inequalities.
• Mass generation in the large \(N\) Gross-Neveu-model

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