Coherent States Associated to the Jacobi Group and Berezin Quantization of the Siegel-Jacobi Ball

摘要

Coherent states are associated to the Jacobi group. The metric obtained from the scalar product of coherent states based on the Siegel-Jacobi ball is a balanced metric. Several geometric properties of the Siegel-Jacobi ball are obtained via the methods of coherent states. We insist on geometric properties of the Siegel-Jacobi ball specific to Berezin quantization.