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

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

2009-12-21

arxiv.org/abs/0912.4223v1

Rev. Math. Phys. 23(4): 375--407, 2011

Physics

Mathematical Physics

55 pages

Scientific paper

10.1142/S0129055X11004321

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/\pi.

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