Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

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, $\Lambda$, 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 $e^{-2}2/\pi$.

37 pages

References in corpus (2)

• Spectral Renormalization Group
• Spectral Analysis of the Semi-relativistic Pauli-Fierz Hamiltonian

Cited by in corpus (8)

• The mass shell in the semi-relativistic Pauli-Fierz model
• Existence of ground states of hydrogen-like atoms in relativistic QED I: The semi-relativistic Pauli-Fierz operator
• On enhanced binding and related effects in the non- and semi-relativistic Pauli-Fierz models
• Existence of ground states of hydrogen-like atoms in relativistic QED II: The no-pair operator
• Self-adjointness of semi-relativistic Pauli-Fierz Hamiltonian
• On the non-relativistic limit of a model in quantum electrodynamics
• Spectrum of the semi-relativistic Pauli-Fierz model I
• Functional integral approach to semi-relativistic Pauli-Fierz models