Coherent States Associated to the Jacobi Group—A Variation on a Theme by Erich Kähler

Abstract

Using the coherent states attached to the complex Jacobi group—the semi-direct product of the Heisenberg-Weyl group with the real symplectic group—we study some of the properties of coherent states based on the manifold which is the product of the $n$-dimensional complex plane with the Siegel upper half plane.