Berry phases and connection matrices defined on homogeneous spaces attached to Siegel-Jacobi groups

Abstract

The relation between the Berry phase and connection matrix on the Siegel-Jacobi disk $\mathcal{D}^J_1$ and Siegel-Jacobi upper half-plane$\mathcal{X}^J_1$ are analyzed. The connection matrix and the covariant derivative of one-forms on the extended Siegel-Jacobi upper half-plane $\tilde{\mathcal{X}}^J_1$ are calculated.