FERMI-LIQUID AS A RENORMALIZATION-GROUP FIXED-POINT - THE ROLE OF INTERFERENCE IN THE LANDAU CHANNEL

We apply the finite-temperature renormalization group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation-invariant Fermi surface. The basic quantities of Fermi- liquid theory, the Landau function, and the scattering vertex are calc ulated as fixed points of the RG flow in terms of the effective action 's interaction function. The classic derivations of Fermi-liquid theor y, which apply the Bethe-Salpeter equation and amount to summing direc t panicle-hole ladder diagrams. neglect the zero-angle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on this components of the Landau functio n. We show that the strong interference of the direct and exchange pro cesses of particle-hole scattering near zero angle invalidates the lad der approximation in this region, resulting in temperature-dependent n arrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied, The consequences of the RG corrections on Fermi-liquid theory are discusse d. In particular, we show that the amplitude sum rule is not valid.