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Existence of atoms and molecules in non-relativistic quantum electrodynamics. (English) Zbl 1058.81080

Summary: We show that the Hamiltonian describing \(N\) nonrelativistic electrons with spin, interacting with the quantized radiation field and several fixed nuclei with total charge \(Z\) has a ground state when \(N <Z+1\). The result holds for any value of the fine structure constant alpha and for any value of the ultraviolet cutoff Lambda on the radiation field. There is no infrared cutoff. The basic mathematical ingredient in our proof is a novel way of localizing the electromagnetic field in such a way that the errors in the energy are of smaller order than \(1/L\), where \(L\) is the localization radius.

MSC:

81V45 Atomic physics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81V10 Electromagnetic interaction; quantum electrodynamics
81V55 Molecular physics
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