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.
Publié le : 1996-07-05
Classification:
rigorous renormalization group methods,
multiscale cluster expansions,
MSC: 81T08;82B28;81T17; 05A19,
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th],
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00087610,
author = {Abdesselam, A. and Rivasseau, V.},
title = {An Explicit Large Versus Small Field Multiscale Cluster Expansion},
journal = {HAL},
volume = {1996},
number = {0},
year = {1996},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00087610}
}
Abdesselam, A.; Rivasseau, V. An Explicit Large Versus Small Field Multiscale Cluster Expansion. HAL, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/hal-00087610/