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
presented.

Event sponsored by:
		University of Bialystok