IMPROVED POWER COUNTING AND FERMI-SURFACE RENORMALIZATION

The naive perturbation expansion for many-fermion systems is infrared divergent. One can remove these divergences by introducing counterterm s. To do this without changing the model, one has to solve an inversio n equation. We call this procedure Fermi surface renormalization (FSR) . Whether or not FSR is possible depends on the regularity properties of the fermion self-energy. When the Fermi surface is nonspherical, th is regularity problem is rather nontrivial. Using improved power count ing at all orders in perturbation theory, we have shown sufficient dif ferentiability to solve the FSR equation for a class of models with a non-nested, non-spherical Fermi surface. I will first motivate the pro blem and give a definition of FSR, and then describe the combination o f geometric and graphical facts that lead to the improved power counti ng bounds. These bounds also apply to the four-point function. They im ply that only ladder diagrams can give singular contributions to the f our-point function.