Existence of Hamiltonians for Some Singular Interactions on Manifolds

Abstract

The existence of the Hamiltonians of the renormalized point interactions in two and three dimensional Riemannian manifolds and that of a relativistic extension of this model in two dimensions are proven. Although it is much more difficult, the proof of existence of the Hamiltonian for the renormalized resolvent for the non-relativistic Lee model can still be given. To accomplish these results directly from the resolvent formula, we employ some basic tools from the semigroup theory.

33 pages, no figures

References in corpus (2)

• Nonrelativistic Lee model in three dimensional Riemannian manifolds
• Non-relativistic Lee Model on two Dimensional Riemannian Manifolds

Cited by in corpus (7)

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• On Schrödinger Operators Modified by $\delta$ Interactions
• Rank One Perturbations Supported by Hybrid Geometries and Their Deformations
• Completeness Relation in Renormalized Quantum Systems