Existence of Hamiltonians for some singular interactions on manifolds

Dogan C., Erman F., Turgut O. T.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.53, sa.4, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 4
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1063/1.4705291
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • İstanbul Üniversitesi Adresli: Evet

Özet

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) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705291]