Existence of ground states of hydrogen-like atoms in relativistic QED I: The semi-relativistic Pauli-Fierz operator

Abstract

We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of the semi-relativistic Pauli-Fierz operator and prove that the infimum of the spectrum of the latter operator is an eigenvalue. In particular, we verify that the bottom of its spectrum is strictly less than its ionization threshold. These results hold true for arbitrary values of the fine-structure constant and the ultra-violet cut-off as long as the Coulomb coupling constant (i.e. the product of the fine-structure constant and the nuclear charge) is less than 2/π.

55 pages

References in corpus (2)

• Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics
• Spectral Renormalization Group

Cited by in corpus (6)

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• The mass shell in the semi-relativistic Pauli-Fierz model
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• On enhanced binding and related effects in the non- and semi-relativistic Pauli-Fierz models
• Self-adjointness of semi-relativistic Pauli-Fierz Hamiltonian
• Existence of ground states of hydrogen-like atoms in relativistic QED II: The no-pair operator