Conference talk Holger Waalkens

Holger Waalkens
Scattering monodromy

The Liouville-Arnold theorem states that a compact preimage of regular value of the energy momentum map of a Liouville integrable system is an f-dimensional torus where f is the number of degrees of freedom, and in the neighbourhood of this torus one can construct action-angle variables. Isolated singular values of the energy momentum map can cause a twist in the torus bundle over the regular image of an energy momentum map. As a result action-angle variables cannot be defined globally. This obstruction to the global construction of action-angle variables has been coined Hamiltonian monodromy, and many prominent examples of Liouville-integrable systems exhibiting this obstruction have been studied in recent years. Through the Bohr-Sommerfeld quantization of action variables monodromy carries over to quantum mechanics where it causes an obstruction to the global existence of quantum numbers. In this talk we discuss the classical and quantum mechanical implications of monodromy for scattering systems, i.e. for Liouville integrable systems where the pre images of the energy momentum map are not compact.
As an example we study Euler's problem of two fixed centers.

Wednesday, April 16, 2014 - 16:50 - 17:10