Interacting Fermi liquid in three dimensions at finite temperature: Part I: Convergent Contributions

Details Interacting Fermi liquid in three dimensions at finite temperature: Part I: Convergent Contributions Interacting Fermi liquid in three dimensions at finite temperature: Part I: Convergent Contributions

2000-12-14

arxiv.org/abs/cond-mat/0012270v1

Physics

Condensed Matter

Superconductivity

85 pages, 13 figures

Scientific paper

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.

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