Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 213

Quantum Electrodynamics of Confined Non-Relativistic Particles

V. Bach, J. Froehlich, I. Sigal

We consider a system of finitely many non-relativistic, quantum mechanical electrons bound to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; but we impose an ultraviolet cutoff on the electromagnetic vector potential appearing in covariant derivatives, and the interactions between the radiation field and electrons localized very far from the nuclei are turned off. For a class of Hamiltonians we prove exponential localization of bound states, establish the existence of a ground state, and derive sufficient conditions for its uniqueness. Furthermore, we show that excited bound states of the unperturbed system become unstable and turn into resonances when the electrons are coupled to the radiation field, by using a novel renormalization transformation which acts directly on the space of Hamiltonians.

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