The collective elementary excitations of a system of Bose-Einstein condensed two-dimensional magnetoexcitons interacting with electron-hole(e-h) plasma in a strong perpendicular magnetic field are studied. The breaking of the gauge symmetry is introduced into the Hamiltonian following the Bogoliubov`s theory of quasiaverages. The motion equations for the summary operators describing the creation and annihilation of magnetoexcitons as well as the density fluctuations of the electron-hole(e-h) plasma were derived. They suggest the existence of magneto-exciton-plasmon complexes, the energies of which differ by the energies of one or two plasmon quanta. Starting with these motion equations one can study the Bose-Einstein Condensation (BEC) of different magneto-exciton-plasmon complexes introducing different constants of the broken symmetry correlated with their energies. The Green`s functions constructed from these summary operators are two-particle Green`s functions. They obey the chains of equations expressing the two-particle Green`s functions through the four-particle and six-particle Green`s functions. These chains were truncated in such a way that the six-particle Green`s functions, were expressed through the two-particle ones. At the same time the elementary excitations with different wave vectors were decoupled. As a result of these simplifications the Dyson-type equation in a matrix form for the two-particle Green`s functions was obtained. The 4x4 determinant constructed from the self-energy part Σij(Pω)gives rise to dispersion equation. The dispersion relations were obtained in analytical form, when in the self-energy parts Σij(Pω) only the terms linear in Coulomb interaction were kept. Taking into account also the terms quadratic in Coulomb interaction the dispersion equation becomes cumbersome and it can be solved only numerically.
Moldavian Journal of the Physical Sciences, Vol.4, N2, 2005, pp. 142-196