- 96-325 Manfred Salmhofer
- Improved Power Counting and Fermi Surface Renormalization
(140K, uuencoded gzipped postscript)
Jul 4, 96
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Abstract. The naive perturbation expansion for many-fermion systems is
infrared divergent. One can remove these divergences by introducing
counterterms. To do this without changing the model, one has to
solve an inversion 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, this regularity problem
is rather nontrivial. Using improved power counting
at all orders in perturbation theory,
we have shown sufficient differentiability to solve the FSR equation
for a class of models with a non-nested, non-spherical Fermi surface.
I will first motivate the problem and give a definition of FSR,
and then describe the combination of geometric and graphical facts
that lead to the improved power counting bounds.
These bounds also apply to the four--point function. They imply
that only ladder diagrams can give singular contributions to
the four--point function.