MPEJ Volume 1, No.3, 28pp Received: September 8, 1995, Revised: October 16, 1995, Accepted: October 23, 1995 Jacques Magnen, Vincent Rivasseau A Single Scale Infinite Volume Expansion for Three Dimensional Many Fermion Green's Functions ABSTRACT: In [FMRT1] we introduced a cluster expansion for many Fermion systems in two space dimensions based on a so-called sector decomposition. In this paper a completely different expansion is introduced to treat the more difficult case of three (or more) space dimensions: it is based on an auxiliary scale decomposition and the use of the Hadamard inequality. We prove that the perturbative expansion for a single scale model has a convergence radius independent of the scale. This is a typical result, proved in the two dimensional case in [FMRT1], which we cannot obtain in three dimensions by naive extrapolation of the sector method. Although we do not treat in this paper the full (multiscale) system, we hope this new method to be a significant step towards the rigorous construction of the BCS theory of superconductivity in three space dimensions.