Connection matrices and Berry phases on the homogeneous spaces ${\mathcal{D}}_1^J$ and ${\mathcal{X}}_1^J$ attached to Jacobi groups

Abstract

We analyze the relation between connection matrices and Berry phases on the Siegel-Jacobi disk ${\mathcal{D}}_1^J$ and Siegel-Jacobi upper half-plane ${\mathcal{X}}_1^J$ and we explicitly compute the connection matrices and the Berry connections on these homogeneous spaces in different coordinates.

23 pages