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 ${\mathcal{D}}_1^J$ and Siegel-Jacobi upper half-plane${\mathcal{X}}_1^J$ are analyzed. The connection matrix and the covariant derivative of one-forms on the extended Siegel-Jacobi upper half-plane ${\tilde{\mathcal{X}}}_1^J$ are calculated.

arXiv comment49 pages, Latex, amsart, AMS fonts. The content of the paper is the same as that of paper arXiv:2401.03758v2, except for 9 minor changes in some formulas at pages 16, 17