A RENORMALIZATION-GROUP APPROACH FOR MANY-FERMION PROBLEMS

A renormalization group transformation (RGT) that permits us to analyze the stability of fermionic systems to various perturbations in any number of dimensions is developed. An RGT that leaves invariant the free fermion system (on or off a lattiice) is defined and interactions are classified as relevent, irrelevent or marginal. It is shown how the RGT automatically considers competing instabilities simultaneously, in contrast to mean field theory, which focuses on just one. It is shown that at weak coupling only the BCS coupling is relevent unless there is nesting. Both Landau theory and the Kohn-Luttinger argument are discussed in this context.