An explicit large versus small field multiscale cluster expansion

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 inde pedent, but for simplicity we chose the infrared phi(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 four point functions, are shown to satisfy the polymer bound.