In this talk we consider the Pauli-Fierz model for a finite number of nonrelativistic electrons in an external electrostatic potential interacting with the quantized, ultraviolet cutoff electromagnetic field. The semigroup generated by the corresponding Hamiltonian has a Fock space operator-valued integral kernel. We study the differentiability properties of this kernel, with respect to time and electron positions, away from the singularities of the electrostatic potential. We further obtain new decay and regularity results on possible ground state eigenvectors and more general elements of spectral subspaces. The proofs of our results are based on Feynman-Kac formulas and an analysis of the differentiability properties of solutions to certain stochastic differential equations associated with the Pauli-Fierz model. These equations have been introduced by Batu Güneysu, Jacob Schach Møller and the present author in an earlier work.
This talk is part of series of talks affiliated with the virtual Mittag-Leffler workshop "Scattering, microlocal analysis and renormalization", organized by Claudio Dappiaggi, Jacob Schach Møller and Michal Wrochna. The full schedule can be found at: