FERMI-LIQUID THEORY - A RENORMALIZAITON GROUP-APPROACH

We show how Fermi liquid theory results can be systematically recovere d using a renormalization group (RG) approach. Considering a two-dimen sional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function Gamma in the limi t of small momentum (Q) and energy (Omega) transfer and obtain the equ ation which determines the collective modes of a Fermi liquid. The den sity-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters F-l(s) and F-l(a)) is determ ined by the fixed point value of the Omega-limit of the two-particle v ertex function (Gamma(Omega). We show how the results obtained at one -loop order can be extended to all orders in a loop expansion. Calcula ting the quasi-particle life-time and renormalization factor at two-lo op order, we reproduce the results obtained from two-dimensional boson ization or Ward Identities. We discuss the zero-temperature limit of t he RG equations and the difference between the Field Theory and the Ka danoff-Wilson formulations of the RG. We point out the importance of n -body (n greater than or equal to 3) interactions in the latter.