Abstract
We consider Dirichlet realizations of Pauli-Fierz type operators generating the dynamics of non-relativistic matter particles which are confined to an arbitrary open subset of the Euclidean position space and coupled to quantized radiation fields. We find sufficient conditions under which their domains and a natural class of operator cores are determined by the domains and operator cores of the corresponding Dirichlet-Schrödinger operators and the radiation field energy. Our results also extend previous ones dealing with the entire Euclidean space, since the involved electrostatic potentials might be unbounded at infinity with local singularities that can only be controlled in a quadratic form sense, and since locally square-integrable classical vector potentials are covered as well. We further discuss Neumann realizations of Pauli-Fierz type operators on Lipschitz domains.
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The author is grateful for support by the VILLUM foundation via the project grant “Spectral Analysis of Large Particle Systems”, and for support by the International Network Programme grant “Exciting Polarons” from the Danish Ministry for Research and Education.
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Matte, O. Pauli-Fierz Type Operators with Singular Electromagnetic Potentials on General Domains. Math Phys Anal Geom 20, 18 (2017). https://doi.org/10.1007/s11040-017-9249-x
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DOI: https://doi.org/10.1007/s11040-017-9249-x