- 97-414 Bach V., Froehlich J., Sigal I.M.
- Quantum Electrodynamics of Confined Nonrelativistic Particles
-- Revised Version
Jul 24, 97
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Abstract. We consider a system of finitely many nonrelativistic,
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. To this end we develop
a novel renormalization transformation which acts
directly on the space of Hamiltonians.