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We apply the finite-temperature renormalization-group (RG) to a model basedon an effective action with a short-range repulsive interaction and a rotationinvariant Fermi surface. The basic quantities of Fermi liquid theory, theLandau function and the scattering vertex, are calculated as fixed points ofthe RG flow in terms of the effective action's interaction function. Theclassic derivations of Fermi liquid theory, which apply the Bethe-Salpeterequation and amount to summing direct particle-hole ladder diagrams, neglectthe zero-angle singularity in the exchange particle-hole loop. As aconsequence, the antisymmetry of the forward scattering vertex is notguaranteed and the amplitude sum rule must be imposed by hand on the componentsof the Landau function. We show that the strong interference of the direct andexchange processes of particle-hole scattering near zero angle invalidates theladder approximation in this region, resulting in temperature-dependentnarrow-angle anomalies in the Landau function and scattering vertex. In this RGapproach the Pauli principle is automatically satisfied. The consequences ofthe RG corrections on Fermi liquid theory are discussed. In particular, we showthat the amplitude sum rule is not valid.Comment: 25 pages, RevTeX 3.

Fermi liquid as a renormalization-group fixed point: The role of interference in the Landau channel