Coherent states and geometry on the Siegel-Jacobi disk

摘要

The coherent state representation of the Jacobi group G_1~J is indexed with two parameters, μ(= 1), describing the part coming from the Heisenberg group, and k, characterizing the positive discrete series representation of SU(1,1). The Ricci form, the scalar curvature and the geodesics of the Siegel-Jacobi disk 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 Siegel-Jacobi disk are presented.