96-684 Joel Feldman, Manfred Salmhofer, and Eugene Trubowitz

Perturbation Theory around Non--Nested Fermi Surfaces II. Regularity of the Moving Fermi Surface: RPA Contributions (436K, uuencoded gzipped postscript) Dec 21, 96

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Abstract. Regularity of the deformation of the Fermi surface under short-range interactions is established for all contributions to the RPA self-energy (it is proven in an accompanying paper that the RPA graphs are the least regular contributions to the self--energy). Roughly speaking, the graphs contributing to the RPA self-energy are those constructed by contracting two external legs of a four-legged graph that consists of a string of bubbles. This regularity is a necessary ingredient in the proof that renormalization does not change the model. It turns out that the self-energy is more regular when derivatives are taken tangentially to the Fermi surface than when they are taken normal to the Fermi surface. The proofs require a very detailed analysis of the singularities that occur at those momenta $\p$ where the Fermi surface $S$ is tangent to $S+\p$. Models in which $S$ is not symmetric under the reflection $\p \to -\p$ are included.

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