  In the present work the Chern-Simons(C-S) gauge field theory developed by
Jackiw and Pi [1] and widely used to explain the fractional quantum Hall
effects, was applied to describe the two-dimensional (2D) electron-hole (e-h)
system in a strong perpendicular magnetic field under the influence of the
quantum point vortices creating the Chern-Simons(C-S) gauge field. The
composite particles formed by electrons and by holes with equal integer
positive numbers of the attached quantum point vortices are described by the
dressed field operators, which obey to the Fermi or to the Bose statistics
depending on the even or odd numbers . It is shown that the phase operators as
well as the vector and the scalar potentials of the C-S gauge field depend on
the difference of the electron and of the hole density operators. They vanish
in the mean field approximation, when the average values of the electron and of
the whole densities coincide. Nevertheless, even in this case, the quantum
fluctuations of the C-S gauge field lead to new physics of the 2D e-h system.
