Quantization of symmetric domains including super-symmetry
by
Harald Upmeier
University of Marburg
Coauthors: Jonathan Arazy, University of Haifa, Israel

For hermitian symmetric domains (Cartan domains) including the flat Fock space we construct the so-called geodesic calculus which generalizes the standard quantization methods (Berezin calculus, Weyl calculus etc) in a uniform way, based on covariance properties of the geodesic symmetries of the underlying domain. For domains of rank one, a complete analysis including the spectral decomposition of the Berezin transform is given in terms of hypergeometric functions. These concepts and results are then extended to the super-symmetric situation involving Bergman spaces of super-holomorphic functions.

Date received: March 29, 2005