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In the present work the Chern-Simons(C-S) gauge field theory developed byJackiw and Pi [1] and widely used to explain the fractional quantum Halleffects, was applied to describe the two-dimensional (2D) electron-hole (e-h)system in a strong perpendicular magnetic field under the influence of thequantum point vortices creating the Chern-Simons(C-S) gauge field. Thecomposite particles formed by electrons and by holes with equal integerpositive numbers of the attached quantum point vortices are described by thedressed field operators, which obey to the Fermi or to the Bose statisticsdepending on the even or odd numbers . It is shown that the phase operators aswell as the vector and the scalar potentials of the C-S gauge field depend onthe difference of the electron and of the hole density operators. They vanishin the mean field approximation, when the average values of the electron and ofthe whole densities coincide. Nevertheless, even in this case, the quantumfluctuations of the C-S gauge field lead to new physics of the 2D e-h system.

Two-dimensional electron-hole system under the influence of the Chern-Simons gauge field created by the quantum point vortices