HOLSTEIN-PRIMAKOFF REALIZATIONS ON COADJOINT ORBITS

We derive the Holstein-Primakoff oscillator realization on the coadjoi nt orbits of the SU(N + 1) and SU(1, N) group by treating the coadjoin t orbits as a constrained system and performing the symplectic reducti on. By using the action-angle variables transformations, we transform the original variables into Darboux variables. The Holstein-Primakoff expressions emerge after quantization in a canonical manner with a sui table normal ordering. The corresponding Dyson realizations are also o btained and some related issues are discussed.