The renormalized Bogoliubov–Fröhlich Hamiltonian

The Bogoliubov–Frohlich Hamiltonian models the interaction of an impurity with the excitations of a Bose–Einstein condensate. It has been observed that the dependence of the ground state energy on the ultraviolet (UV) cutoff differs significantly from what would be expected from similar well-known models. We give a detailed explanation of this UV behavior and provide an explicit representation of the renormalized Hamiltonian.