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Existence and Construction of Resonances for Atoms Coupled to the Quantized Radiation Field

Mathematical Physics & Probability

Speaker: Miguel Ballesteros, Technische Universit ̈at Braunschweig
Location: 2112 MSB
Start time: Wed, Jun 6 2012, 4:10PM

We analyze the Pauli-Fierz model, which represents a non- relativistic atom coupled to a (quantized) photon field. We prove that the excited eigenvalues of the atom give rise to resonances, once the photon field is introduced, and that the energies of the resonance- producing photons are given by Bohr’s frequency condition, up to second order in the coupling constant. We do not assume that there is an infrared regularization but we require an ultraviolet cutoff. We review Sigal’s recent construction of resonances based on renormalization group analysis and present a novel alternative construction based on iterative analytic perturbation theory. This is a joint work with Volker Bach and Alessandro Pizzo.