The Jacobi Group and the Squeezed States—Some Comments
Abstract
The generalized coherent states attached to the Jacobi group realize the squeezed states. Imposing hermitian conjugacy to the generators of the Jacobi algebra, we find the form of the weight function appearing in the scalar product. We show effectively the orthonormality of the base functions with respect to the scalar product. From the explicit form of the reproducing kernel, we find the expression for the multiplier in a holomorphic representation of the Jacobi group.
 Publication:

XXVIII Workshop on Geometrical Methods in Physics
 Pub Date:
 November 2009
 DOI:
 10.1063/1.3275594
 arXiv:
 arXiv:0910.5563
 Bibcode:
 2009AIPC.1191...21B
 Keywords:

 algebra;
 squeezed states;
 optical;
 numerical analysis;
 02.20.Sv;
 42.50.Dv;
 02.60.x;
 Lie algebras of Lie groups;
 Nonclassical states of the electromagnetic field including entangled photon states;
 quantum state engineering and measurements;
 Numerical approximation and analysis;
 Mathematics  Differential Geometry;
 Mathematical Physics;
 Mathematics  Representation Theory;
 Physics  Optics;
 81R30;
 32Q15;
 20C35;
 81V80
 EPrint:
 9 pages, to appear in AIP Conference Proceedings, Geometric Methods In Physics, Bialowieza (Poland), June 28 July 4 2008, Editor(s): P. Kielanowski, S. T. Ali, A. Odzijewicz, M. Schlichenmaier, Th. Voronov