Stone-von Neumann Theorem in Quantum Geometry
by
Christian Fleischhack
Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, 04103 Leipzig, Germany

The configuration space of quantum geometry is the compact space [`(A)] of distributional connections in a principal fibre bundle P with compact structure group. The corresponding Weyl algebra A is generated by the continuous functions on [`(A)] and the pull-backs of certain homeomorphisms on [`(A)]. The latter ones correspond to the left translations generated by the momenta in quantum mechanics. Recently, it has been shown that there is (up to unitary equivalence) only one regular representation of A having a cyclic and diffeomorphism invariant vector. Additional assumptions concern the dimension of the base manifold M of P (at least three) and how the action of diffeomorphisms on M is lifted to the representation space. In this talk, the main ideas of the proof are going to be discussed.

Date received: March 28, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caql-88.