Differential operators on orbits of coherent states

Abstract

We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space attached to the dual of the Hilbert space of the representation. This permits a realization by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits.

10 pages. Submitted to the Proceedings of the First National Romanian Conference on Theoretical Physics, September 13-16, 2002, Magurele, Bucharest, Romania

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• A holomorphic representation of the Jacobi algebra
• Realization of coherent state Lie algebras by differential operators
• A convenient coordinatization of Siegel-Jacobi domains
• Balanced Metric and Berezin Quantization on the Siegel-Jacobi Ball
• Bergman representative coordinates on the Siegel-Jacobi disk
• Geometrical phases on hermitian symmetric spaces
• The Real Jacobi Group Revisited
• Hamiltonian systems on almost cosymplectic manifolds
• Linear Hamiltonians on homogeneous Kähler manifolds of coherent states