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We discuss an approach to higher dimensional bosonization of interactingfermion s based on a picture of fluctuating Fermi surface. Compared with thelinearized"constructive" approach developed in Refs.[9-11] this method allowsan account of the Fermi surface curvature due to nongaussian terms in thebosonized Lagrangian. On the basis of this description we propose a procedureof calculating density response functions beyond the random phaseapproximation. We also formulate a bosonic theory of the compressiblemetal-like state at half filled lowest Landau level and check that in gaussianapproximation it reproduces RPA results of the gauge theory by Halperin, Lee,and Read.Comment: 23 pages, Latex 3.0, Princeton preprin

Geometrical approach to bosonization ofD>1 dimensional (non)-Fermi liquids