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Point perturbations in constant curvature spaces. (English) Zbl 1190.83010
Summary: Point perturbations of the free Hamiltonian in two- and three-dimensional spaces of constant curvatures are considered. The study of the spectral properties of perturbed Hamiltonian and various asymptotics for its point levels are presented. It is shown that the binding energy in comparison with the case of zero curvature reduces in the case of Lobachevsky plane and rises in the case of 2D-sphere, when the scattering length is much less than the curvature radius.

MSC:
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C47 Methods of quantum field theory in general relativity and gravitational theory
81T20 Quantum field theory on curved space or space-time backgrounds
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