An Explicit Large Versus Small Field Multiscale Cluster Expansion

Details An Explicit Large Versus Small Field Multiscale Cluster Expansion An Explicit Large Versus Small Field Multiscale Cluster Expansion

1996-05-14

arxiv.org/abs/hep-th/9605094v1

Rev.Math.Phys.9:123-199,1997

Physics

High Energy Physics

High Energy Physics - Theory

65 pages, LaTeX

Scientific paper

10.1142/S0129055X97000063

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.

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