Teoman Turgut: Heat Kernels in Some Singular Problems

We discuss some simple singular quantum mechanical models. We present briefly attractive delta function potentials on two dimensional manifolds and the associated renormalization group equation. It is well known that these problems suffer from a divergence, we show that it can nicely be cured by means of  heat kernel regularization. We extend this model to particles with relativistic dispersion relations. Recently there is some interest for interaction supported over curves, we discuss the same model for particles on two and three dimensional manifolds interacting with delta functions supported over embedded circles. A relativistic generalization is also pointed out. If time permits we will present a many body version of the attractive delta function on a two dimensional manifold.