RESONANT DECAY OF A 2 STATE ATOM INTERACTING WITH A MASSLESS NONRELATIVISTIC QUANTIZED SCALAR FIELD

We consider a model Hamiltonian derived from the interaction of an ato m with a non-relativistic massless quantized field. The model atom has two states, and the interaction is linear in the field operator. We d o not make the rotating wave approximation and there is no infrared cu toff. We prove that the excited state of the atom with no photons pres ent decays at an approximately exponential rate in accordance with the predictions of time dependent perturbation theory. The proof requires some analyticity and regularity assumptions on the interaction betwee n atom and field. These imply in particular that the interaction goes to zero at least as fast as k2, as k --> 0, where k is the photon mome ntum.