Regularity of the moving Fermi surface: the exact selfenergy

Regularity of the deformation of the Fermi surface under short-range interactions is established to all orders in perturbation theory. The proofs are based on a new classification of all graphs that are not doubly overlapping. They turn out to be generalized RPA graphs. This provides a simple extension to all orders of the regularity theorem of the Fermi surface movement proven in [FST2]. Models in which the Fermi surface is not symmetric under the reflection p to -p are included.