  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.
