Interacting Fermi liquid in three dimensions at finite temperature: Part I: Convergent Contributions
arXiv:cond-mat/0012270 · doi:10.1007/s00023-001-8594-1
Abstract
In this paper we complete the first step, namely the uniform bound on completely convergent contributions, towards proving that a three dimensional interacting system of Fermions is a Fermi liquid in the sense of Salmhofer. The analysis relies on a direct space decomposition of the propagator, on a bosonic multiscale cluster expansion and on the Hadamard inequality, rather than on a Fermionic expansion and an angular analysis in momentum space, as was used in the recent proof by two of us of Salmhofer's criterion in two dimensions.
85 pages, 13 figures