An inversion theorem in Fermi surface theory

We prove a perturbative inversion theorem for the map between the interacti ng and the noninteracting Fermi surface for a class of many fermion systems with strictly convex Fermi surfaces and short-range interactions between t he fermions, This theorem gives a physical meaning to the counterterm funct ion K that we use in the renormalization of these models: K can be identifi ed as that part of the self-enerey that causes the deformation of the Fermi surface when the interaction is turned on. (C) 2000 John Wiley & Sons, Inc .