  We propose a (4+1) dimensional Chern-Simons field theoretical description of
the fractional quantum Hall effect. It suggests that composite fermions reside
on a momentum manifold with a nonzero Chern number. Based on derivations from
microscopic wave functions, we further show that the momentum manifold has a
uniformly distributed Berry curvature. As a result, composite fermions do not
follow the ordinary Newtonian dynamics as commonly believed, but the more
general symplectic one. For a Landau level with the particle-hole symmetry, the
theory correctly predicts its Hall conductance at half-filling as well as the
symmetry between an electron filling fraction and its hole counterpart.
