  We present a field theory of Jain's composite fermion model as generalised to
the bilayer quantum Hall systems. We define operators which create composite
fermions and write the Hamiltonian exactly in terms of these operators. This is
seen to be a complexified version of the familiar Chern Simons theory. In the
mean-field approximation, the composite fermions feel a modified effective
magnetic field exactly as happens in usual Chern Simons theories, and plateaus
are predicted at the same values of filling factors as Lopez and Fradkin and
Halperin . But unlike normal Chern Simons theories, we obtain all features of
the first-quantised wavefunctions including its phase, modulus and correct
gaussian factors at the mean field level. The familiar Jain relations for
monolayers and the Halperin wavefunction for bilayers come out as special
cases.
