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Heat kernel approach to singular problems

Teoman Turgut
Boğaziçi University, Istanbul
Monday, December 7, 2015 - 11:30

We discuss the bound state spectrum of a particle moving on a Riemannian manifold under the influence of delta function potentials. We show that the renormalization can be naturally accomplished by the heat kernel approach. A slight generalization to the Klein-Gordon type particles are also presented. Currently there is some interest on particles captured by curves, modeled by singular interactions supported on such curves, we present a generalization to our approach to circles embedded into a Riemannian manifold. We also discuss the renormalization group flows of these systems. If time permits a more ambitious generalization to interacting bosons on a two dimensional manifold will be presented.

Venue: Department of Mathematics, Trieste University, Seminar Room - Third Floor bld H2bis

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