BEC for a coupled two-type hard core bosons model

We study a solvable model of two types hard core Bose particles. A complete analysis is given of its equilibrium states including the proof of existence of Bose–Einstein condensation. The plasmon frequencies and the quantum normal modes corresponding to these frequencies are rigorously constructed. In particular, we show a two-fold degeneracy of these frequencies. We show that all this results from spontaneous gauge symmetry breakdown.