Abstract
We study the properties of Fermi liquids with the microscopic constraint of a local self-energy. In this case the forward scattering sum rule imposes strong limitations on the Fermi-liquid parameters, which rule out any Pomeranchek instabilities---both ferromagnetism and phase separation are suppressed. Superconductivity is possible in an $s$-wave channel only. We also study the approach to the metal-insulator transition, and find a Wilson ratio approaching 2. This ratio and other properties of ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{TiO}}_{3}$ are all consistent with the local Fermi-liquid scenario.
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