Coherent states and geometry on the Siegel-Jacobi disk

Abstract

The coherent state representation of the Jacobi group $G_1^J$ is indexed with two parameters, $\mu (=\frac{1}{\hslash })$, describing the part coming from the Heisenberg group, and $k$, characterizing the positive discrete series representation of $\text{SU}(1,1)$. The Ricci form, the scalar curvature and the geodesics of the Siegel-Jacobi disk ${\mathcal{D}}_1^J$ are investigated. The significance in the language of coherent states of the transform which realizes the fundamental conjecture on the Siegel-Jacobi disk is emphasized. The Berezin kernel, Calabi's diastasis, the Kobayashi embedding, and the Cauchy formula for the Sigel-Jacobi disk are presented.

References in corpus (3)

• Invariant metrics and Laplacians on Siegel-Jacobi space
• On the Bergman representative coordinates
• On the geometry of Siegel-Jacobi domains

Cited by in corpus (2)

• Gaussian distributions, Jacobi group and Siegel-Jacobi space
• Invariant metric on the extended Siegel-Jacobi upper half space