Self-adjointness and domain of the Fröhlich Hamiltonian (Q2795536)

The paper addresses a formal inconsistency of the standard Fröhlich Hamiltonian for the polaron, i.e., a quasi-particle built of an electron interacting with a deformation of a polar crystal into which the electron is immersed. Namely, the self-adjointness of the Hamiltonian is made problematic by the interaction term. Using recently developed operator bounds, developed in terms of general functional analysis, the paper makes use of a specific dressing transform to produce an explicit characterization of the self-adjointness domain.