Differential operators on orbits of coherent states

Details Differential operators on orbits of coherent states Differential operators on orbits of coherent states

2002-11-04

arxiv.org/abs/math/0211054v1

Mathematics

Differential Geometry

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

Scientific paper

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 K\"ahler coherent state orbits.

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