CONSEQUENCES OF THE FUNDAMENTAL CONJECTURE FOR THE MOTION ON THE SIEGEL–JACOBI DISK

Abstract

We find the homogeneous Kähler diffeomorphism FC which expresses the Kähler two-form on the Siegel–Jacobi domain [Formula: see text] as the sum of the Kähler two-form on ℂ and the one on the Siegel ball [Formula: see text]. The classical motion and quantum evolution on [Formula: see text] determined by a linear Hamiltonian in the generators of the Jacobi group [Formula: see text] is described by a Riccati equation on [Formula: see text] and a linear first-order differential equation in z ∈ ℂ, where H 1 denotes the three-dimensional Heisenberg group. When the transformation FC is applied, the first-order differential equation for the variable z ∈ ℂ decouples of the motion on the Siegel disk. Similar considerations are presented for the Siegel–Jacobi space [Formula: see text], where [Formula: see text] denotes the Siegel upper half-plane.

Locations

• International Journal of Geometric Methods in Modern Physics - View
• arXiv (Cornell University) - View - PDF