Alexander Strohmaier (University of Leeds, UK)
A relative Birman-Krein formula in obstacle scattering and its applications
Spectral theory of the Laplace operator on unbounded domains in R^n is conveniently described by stationary scattering theory. One of the major results in this theory is that traces of differences of functions of perturbed and unperturbed operator are related by the spectral shift function. The Birman-Krein formula then allows to express this spectral shift function by the scattering matrix. We show that in the context of many obstacles a relative spectral shift function can be defined that applies to a significantly larger class of functions that even includes unbounded functions of polynomial growth. In the talk I will explain the basic notions such as scattering matrix, spectral shift function, state the main result, and give applications in quantum field theory.
Joint work with F. Hanisch and A. Waters