Erman, FatihTurgut, O. Teoman2017-04-192017-04-192013Erman, F., and Turgut, O.T. (2013). A many-body problem with point interactions on two-dimensional manifolds. Journal of Physics A: Mathematical and Theoretical, 46(5). doi:10.1088/1751-8113/46/5/055401.1751-81131751-8121https://doi.org/10.1088/1751-8113/46/5/055401https://hdl.handle.net/11147/5341A 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.eninfo:eu-repo/semantics/openAccessBosonsRenormalizationQuantum mechanicsBound statesRenormalization group equationsWavefunctionArticle2-s2.0-8487312386210.1088/1751-8113/46/5/05540110.1088/1751-8113/46/5/055401