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Selfadjointness and Domain of the Fröhlich Hamiltonian

Selfadjointness and Domain of the Fröhlich Hamiltonian

Datum: 4. Juli 2017 13:15

Ort: NWZ II, Raum 4.331, Pfaffenwaldring 57, Stuttgart-Vaihingen

Selfadjointness and Domain of the Fröhlich Hamiltonian
Andreas Wünsch, Universität Stuttgart

In the large polaron model of H. Fröhlich, the electron-phonon interaction is a small perturbation in form sense, but a large perturbation in operator sense. This means that the form-domain of the Hamiltonian is not affected by the interaction but the domain of self-adjointness is. We are nevertheless able, to give an explicit characterization of the domain in terms of a suitable dressing transform. Using the mapping properties of this dressing transform, we analyse the smoothness of vectors in the domain of the Hamiltonian with respect to the position of the electron.

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