CROSSOVER FROM LUTTINGER TO FERMI-LIQUID BY INCREASING DIMENSION

We analyzed the dimensional crossover from the Luttinger liquid to the Fermi liquid in continuous dimensions d between one and two by using Ward Identities for the density vertices. It is shown that the Fermi l iquid is stable with respect to residual small q scattering by non sin gular interactions in any d > 1. Long range forces proportional to 1/\ q\(alpha) modify these results for alpha greater than or equal to 2d - 2. Finally the relation between the above analysis and the method of bosonization in d = 2 is discussed.