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
- E-Print:
- 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