Spectral analysis of relativistic atoms – interaction with the quantized radiation field

Abstract

This is the the second part of a series of two papers, which investigate spectral properties of Dirac operators with singular potentials. We will provide a spectral analysis of a relativistic one-electron atom in interaction with the second quantized radiation field and thus extend the work of Bach, Fröhlich, and Sigal [5] and Hasler, Herbst, and Huber[19] to such systems. In particular, we show that the lifetime of excited states in a relativistic hydrogen atom coincides with the life time given by Fermi’s Golden Rule in the non-relativistic case. We will rely on the technical preparations derived in the first part [25] of this work.