SEM

[Ludwik Dabrowski]

Prof. Teoman Turgut  (Bogazici Univ., Istanbul)

"Simple singular interaction on manifolds"

Monday, December 5, 11:00 a.m, Room 134, SISSA

Abstract:
Delta functions on two and three dimensional manifolds are examples
of singular interactions which require renormalization at a simple level. 
We will prove that for certain classes of manifolds after renormalization
the energy is bounded from below. We will discuss an analog of Sturm
comparison theorem. The ground state wave function is always positive
hence nondegenerate as in the usual potential problems.
We will comment on the decay of bound state wave functions.
We will show that one can introduce a beta-function which is negative.
If time permits we will talk about a related model, a single spin 
system interacting with relativistic bosons in two dimensions.
We will prove that the energy is bounded from below.