On the Ultraviolet Limit of the Pauli-Fierz Hamiltonian in LL- and in BHF-Approximation
We consider a quantum mechanical system consisting of a nonrelativistic particle that is minimally coupled to the quantized radiation field, but in absence of external fields that would bind the particle. Even though this model is not relativistically covariant, it is assumed to yield some insight into the nature of the ultraviolet problem of QED, from an analytic point of view.
The talk starts with a review of the model described above and of the results that have been obtained in the past three decades on it. One focus lies on the LL model that had been introduced by Lieb and Loss in 1999 and has been fully characterized recently. A second focus lies on the Bogoliubov-Hartree-Fock (BHF) approximation for the system at zero total momentum for which recent results achieved with M. Ballesteros, S. Breteaux, M. Herdzik, M. Mlinarzik, and T. Tzaneteas are presented.
