Geometrical Approach to Bosonization of D>1 Dimensional (Non) Fermi Liquids

We discuss an approach to higher dimensional bosonization of interacting fermion s based on a picture of fluctuating Fermi surface. Compared with the linearized"constructive" approach developed in Refs.[9-11] this method allows an account of the Fermi surface curvature due to nongaussian terms in the bosonized Lagrangian. On the basis of this description we propose a procedure of calculating density response functions beyond the random phase approximation. We also formulate a bosonic theory of the compressible metal-like state at half filled lowest Landau level and check that in gaussian approximation it reproduces RPA results of the gauge theory by Halperin, Lee, and Read.