An Explicit Large Versus Small Field Multiscale Cluster Expansion

Abstract

We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just renormalizable theory, and allows the writing of explicit non-perturbative formulas for the Schwinger functions. The procedure is quite model independent, but for simplicity we chose the infrared $\ph^4_4$ model as a testing ground. We used also a large field versus small field expansion. The polymer amplitudes, corresponding to graphs without almost local two and for point functions, are shown to satisfy the polymer bound.

65 pages, LaTeX

References in corpus (3)

• Trees, forests and jungles: a botanical garden for cluster expansions
• On Renormalization Group Flows and Polymer Algebras
• A Single Slice 2d Anderson Model at Weak Disorder

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