Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

Details Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

2009-04-20

arxiv.org/abs/0904.3083v1

Commun. Math. Phys. 295: 551--583, 2010

Physics

Mathematical Physics

37 pages

Scientific paper

10.1007/s00220-009-0946-6

We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, $e^2$, and the ultra-violet cut-off, $\Lambda$, and for all nuclear charges less than the critical charge without radiation field, $Z_c=e^{-2}2/(2/\pi+\pi/2)$. We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of $e^2$ and $\Lambda$ and for nuclear charges less than $e^{-2}2/\pi$.

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