Based upon the hidden Lie SU(1,1) symmetry, we have constructed the un
itary decoupling transformation which diagonalizes the multimode two-q
uantum Jaynes-Cummings model and provides us with an extremely conveni
ent basis to gain a deeper understanding of the dressing processes pre
sent in the matter-field interaction. This canonical transformation ap
proach is very simple and can be easily extended to other generalized
Jaynes-Cummings models.