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

STEFAN BERCEANU

Department of Theoretical Physics, Horia Hulubei National Institute for Physics and Nuclear Engineering, P. O. Box MG-6, 077125 Magurele, Romania

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https://doi.org/10.1142/S0219887812500764Cited by:5 (Source: Crossref)

Abstract

We find the homogeneous Kähler diffeomorphism FC which expresses the Kähler two-form on the Siegel–Jacobi domain as the sum of the Kähler two-form on ℂ and the one on the Siegel ball . The classical motion and quantum evolution on determined by a linear Hamiltonian in the generators of the Jacobi group is described by a Riccati equation on and a linear first-order differential equation in z ∈ ℂ, where H₁ 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 , where denotes the Siegel upper half-plane.

Keywords:

AMSC: 81R30, 32Q15, 81V80, 81S10, 34A05

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