Spectral analysis of relativistic atoms – interaction with the quantized radiation field
Documenta mathematica, Tome 14 (2009), pp. 115-156
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.
Classification :
35J99, 35Q40, 81Q10, 81T99, 81V10
Mots-clés : quantum electrodynamics, Dirac-operator, spectral analysis, Fermi golden rule
Mots-clés : quantum electrodynamics, Dirac-operator, spectral analysis, Fermi golden rule
@article{10_4171_dm_267,
author = {Matthias Huber},
title = {Spectral analysis of relativistic atoms {\textendash} interaction with the quantized radiation field},
journal = {Documenta mathematica},
pages = {115--156},
year = {2009},
volume = {14},
doi = {10.4171/dm/267},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/267/}
}
Matthias Huber. Spectral analysis of relativistic atoms – interaction with the quantized radiation field. Documenta mathematica, Tome 14 (2009), pp. 115-156. doi: 10.4171/dm/267
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