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.
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Submitted 15/12/00, accepted 08/02/01
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Disertori, M., Magnen, J. & Rivasseau, V. Interacting Fermi Liquid in Three Dimensions at Finite Temperature: Part I: Convergent Contributions. Ann. Henri Poincaré 2, 733–806 (2001). https://doi.org/10.1007/s00023-001-8594-1
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DOI: https://doi.org/10.1007/s00023-001-8594-1