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

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.
Comment: 28 pages