分野別セミナー

Abstract:
In this talk we consider a physical model for non-relativistic quantum mechanical matter particles interacting with a linearly coupled relativistic radiation field. More than half a century ago Edward Nelson showed that such a model is renormalizable in the sense that a certain ultra-violet cut-off introduced in the corresponding Hamilton operator to render it mathematically well-defined can be removed after a suitable cut-off dependent constant has been subtracted from the Hamiltonian. Our main results are a Feynman-Kac formula for the semi-group generated by the renormalized Hamilton operator and a novel lower bound on the spectrum of the latter.