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)
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.