Resolvent smoothness and local decay at low energies for the standard model of non-relativistic QED

Jean-Francois Bony, Jérémy Faupin

Published 2011-04-15Version 1

We consider an atom interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. The nucleus is supposed to be fixed. We prove smoothness of the resolvent and local decay of the photon dynamics for quantum states in a spectral interval I just above the ground state energy. Our results are uniform with respect to I. Their proofs are based on abstract Mourre's theory, a Mourre inequality established in [FGS1], Hardy-type estimates in Fock space, and a low-energy dyadic decomposition.