DOCUMENTA MATHEMATICA, Vol. 14 (2009), 115-156

Matthias Huber

Spectral Analysis of Relativistic Atoms -- Interaction with the Quantized Radiation Field

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 \cite{Bachetal1999S} and Hasler, Herbst, and Huber \cite{Hasleretal2008} 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 \cite{Huber2008S} of this work.

2000 Mathematics Subject Classification: Primary 81V10; Secondary 35J99, 35Q40, 81Q10, 81T99

Keywords and Phrases: Dirac-Operator, Quantum Electrodynamics, Spectral Analysis, Fermi Golden Rule

Full text: dvi.gz 66 k, dvi 211 k, ps.gz 851 k, pdf 456 k.