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. (C) 2001 Elsevier Science B.V. All rights reserved.