Search Results

Now showing 1 - 2 of 2

Citation - WoS: 2
Citation - Scopus: 3
Renormalization of Dirac Delta Potentials Through Minimal Extension of Heisenberg Algebra
(IOP Publishing Ltd., 2017) Erman, Fatih
We renormalize the model of multiple Dirac delta potentials in two and three dimensions by regularizing it through the minimal extension of Heisenberg algebra. We show that the results are consistent with the other regularization schemes given in the literature.
Citation - WoS: 5
Citation - Scopus: 5
A Many-Body Problem With Point Interactions on Two-Dimensional Manifolds
(IOP Publishing Ltd., 2013) Erman, Fatih; Turgut, O. Teoman
A non-perturbative renormalization of a many-body problem, where non-relativistic bosons living on a two-dimensional Riemannian manifold interact with each other via the two-body Dirac delta potential, is given by the help of the heat kernel defined on the manifold. After this renormalization procedure, the resolvent becomes a well-defined operator expressed in terms of an operator (called principal operator) which includes all the information about the spectrum. Then, the ground state energy is found in the mean-field approximation and we prove that it grows exponentially with the number of bosons. The renormalization group equation (or Callan-Symanzik equation) for the principal operator of the model is derived and the beta function is exactly calculated for the general case, which includes all particle numbers.

Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection