A. Abdesselam et V. Rivasseau, AN EXPLICIT LARGE VERSUS SMALL-FIELD MULTISCALE CLUSTER-EXPANSION, Reviews in mathematical physics, 9(2), 1997, pp. 123-199
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.