Perturbation Theory around Non–Nested Fermi Surfaces II. Regularity of the Moving Fermi Surface: RPA Contributions

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→ −p are included. 1 feldman@math.ubc.ca, http://www.math.ubc.ca/∼feldman/ 2 manfred@math.ethz.ch, http://www.math.ethz.ch/∼manfred/manfred.html 3 trub@math.ethz.ch