AN EXPLICIT LARGE VERSUS SMALL-FIELD MULTISCALE CLUSTER-EXPANSION

We introduce a new type of cluster expansion which generalizes a previ ous formula of Brydges and Kennedy. The method is especially suited fo r performing a phase-space multiscale expansion in a just renormalizab le theory, and allows the writing of explicit non-perturbative formula s for the Schwinger functions. The procedure is quite model inde peden t, but for simplicity we chose the infrared phi(4)(4) model as a testi ng ground. We used also a large field versus small field expansion. Th e polymer amplitudes, corresponding to graphs without almost local two and four point functions, are shown to satisfy the polymer bound.