Perturbation Dynamics of the Infinite Dicke Model

By means of operator algebraic methods the dynamics of the Dicke model is investigated in the limit where the number of the two-level atoms goes to infinity and the interaction strength remains on a finite level. The infinite atomic system is treated as a mean field quantum lattice system. It is shown that the limiting dynamics is essentially determined by the collective behaviour of the atoms. With Trotter's product formula and perturbation theoretical methods we obtain explicit expressions for the unitary time evolution operators in the uncoupled representation.