Existence of Hamiltonians for Some Singular Interactions on Manifolds

Details Existence of Hamiltonians for Some Singular Interactions on Manifolds Existence of Hamiltonians for Some Singular Interactions on Manifolds

2011-11-09

arxiv.org/abs/1111.2168v1

Physics

Mathematical Physics

33 pages, no figures

Scientific paper

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.

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