Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules

In this paper we study the energy spectrum of the Pauli-Fierz Hamiltonian g enerating the dynamics of nonrelativistic electrons bound to static nuclei and interacting with the quantized radiation held, We show that, for suffic iently small values of the elementary electric charge, and under weaker con ditions than those required in [3], the spectrum of this Hamiltonian is abs olutely continuous, except possibly in small neighbourhoods of the ground s tate energy and the ionization thresholds. Tn particular, it is shown that (for a large range of energies) there are no stable excited eigenstates. Th e method used to prove these results relies on the positivity of the commut ator between the Hamiltonian and a suitably modified dilatation generator o n photon Fock space.