  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.
