  We develop a new method for bosonizing the Fermi surface based on the
formalism of the coadjoint orbits. This allows one to parametrize the Fermi
surface by a bosonic field that depends on the spacetime coordinates and on the
position on the Fermi surface. The Wess-Zumino-Witten term in the effective
action, governing the adiabatic phase acquired when the Fermi surface changes
its shape, is completely fixed. As an effective field theory the action also
involves a Hamiltonian which contains, beside the kinetic energy and the Landau
interaction, terms with arbitrary number of derivatives and fields. We show
that the resulting local effective field theory captures both linear and
nonlinear effects in Landau's Fermi liquid theory. The approach can be extended
to incorporate spin degrees of freedom and the charge-2 fields corresponding to
the BCS order parameter.
