Existence of Hamiltonians for Some Singular Interactions on Manifolds
  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. 
\c{C}a\u{g}lar Do\u{g}an, Fatih Erman and O. Teoman Turgut
math-ph math.MP