Wei-Norman and Berezin's equations of motion on the Siegel-Jacobi disk

Abstract

We show that the Wei-Norman method applied to describe the evolution on the Siegel-Jacobi disk ${\mathcal{D}}_1^J={\mathcal{D}}_1\times {\mathbb{C}}^1$, where ${\mathcal{D}}_1$ denotes the Siegel disk, determined by a hermitian Hamiltonian linear in the generators of the Jacobi group $G_1^J$ and Berezin's scheme using coherent states give the same equations of quantum and classical motion when are expressed in the coordinates in which the Kähler two-form ${\omega }_{{\mathcal{D}}_1^J}$ can be written as ${\omega }_{{\mathcal{D}}_1^J}={\omega }_{{\mathcal{D}}_1}+{\omega }_{{\mathbb{C}}^1}$. The Wei-Norman equations on ${\mathcal{D}}_1^J$ are a particular case of equations of motion on the Siegel-Jacobi ball ${\mathcal{D}}_n^J$ generated by a hermitian Hamiltonian linear in the generators of the Jacobi group $G_n^J$ obtained in Berezin's approach based on coherent states on ${\mathcal{D}}_n^J$.

20 pages, Latex, amsart, AMS fonts

References in corpus (6)

• Invariant metrics and Laplacians on Siegel-Jacobi space
• A holomorphic representation of the multidimensional Jacobi algebra
• A holomorphic representation of the Jacobi algebra
• Realization of coherent state Lie algebras by differential operators
• A convenient coordinatization of Siegel-Jacobi domains
• Applications of the Jacobi group to Quantum Mechanics