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Exponential Localization of Hydrogen-like Atoms in Relativistic Quantum Electrodynamics

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Abstract

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, Λ, and for all nuclear charges less than the critical charge without radiation field, Z c  = e −22/(2/π + π/2). We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of e 2 and Λ and for nuclear charges less than e −22/π.

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Authors and Affiliations

  1. Institut für Mathematik, TU Clausthal, Erzstraße 1, 38678, Clausthal-Zellerfeld, Germany

    Oliver Matte

  2. Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstraße 39, 80333, München, Germany

    Oliver Matte & Edgardo Stockmeyer

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  1. Oliver Matte
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  2. Edgardo Stockmeyer
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Correspondence to Oliver Matte.

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Communicated by I.M. Sigal

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Matte, O., Stockmeyer, E. Exponential Localization of Hydrogen-like Atoms in Relativistic Quantum Electrodynamics. Commun. Math. Phys. 295, 551–583 (2010). https://doi.org/10.1007/s00220-009-0946-6

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