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Explicit Derivation of the Propagator for a Point Interaction in Three Dimensional Hyperbolic Space
(Springer/plenum Publishers, 2024) Erman, Fatih
The explicit expression for the propagator of the Dirac delta potential in three dimensional hyperbolic spaces is derived using the integral transform of the Krein's type of the resolvent formula, obtained after the renormalization procedure.
Citation - WoS: 2
Non-Relativistic Lee Model in Two-Dimensional Riemannian Manifolds
(American Institute of Physics, 2012) Erman, Fatih; Turgut, Osman Teoman
This work is a continuation of our previous work [F. Erman and O. T. Turgut, J. Math. Phys. 48, 122103 ( 2007)], where we constructed the non-relativistic Lee model in three-dimensional Riemannian manifolds. Here we renormalize the two-dimensional version by using the same methods and the results are shortly given since the calculations are basically the same as in the three-dimensional model. We also show that the ground state energy is bounded from below due to the upper bound of the heat kernel for compact and Cartan-Hadamard manifolds. In contrast to the construction of the model and the proof of the lower bound of the ground state energy, the mean field approximation to the two-dimensional model is not similar to the one in three dimensions and it requires a deeper analysis, which is the main result of this paper. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705355]

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