XXXII Workshop on Geometric Methods in Physics 30.06-6.07.2013

Stefan Berceanu

Quantum mechanics and geometry on Siegel-Jacobi disk

The Jacobi group is the semidirect product of the real symplectic
group with appropiate Heisenberg group. The Sigel-Jacobi domains are
homogenous K\"ahler manifolds attached to the Jacobi groups. We have introduced
generalized coherent states based on the the Siegel-Jacobi
manifolds. Using a holomorphic representation of the Jacobi algebra by
first order differential operators, we describe the dyamics of a
process generated by a linear Hamiltonian in the generators of the
Jacobi group. The Berezin kernel, Calabi's diastasis, the Kobayashi
embedding, and the Cauchy formula for the Sigel-Jacobi disk are

Event sponsored by:
Belgian Science Policy Office     PAI          University
of Bialystok
University of Bialystok

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