Speaker: Dr. Christian Fleischhack
Title: Stone-von Neumann Theorem in Quantum Geometry
Abstract: In ordinary quantum mechanics the Weyl algebra generated by the exponentiated position and momentum operators, has a unique regular and irreducible representation - the Schroedinger representation. In quantum geometry, a similar argument singles out the Ashtekar-Lewandowski representation. There the Weyl algebra is generated by the parallel transports and the exponentiated fluxes. We will discuss under which assumptions there is only one regular representation having a diffeomorphism invariant and regular vector. If time permits, we compare our results with a similar uniqueness result derived by Lewandowski, Okolow, Sahlmann and Thiemann for the holonomy-flux *-algebra which is built without exponentiating the fluxes.
Talk: Transparencies, Recorded Talk