Coherent state embeddings, polar divisors and Cauchy formulas

Abstract

For arbitrary quantizable compact Kaehler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vectors on the manifold with the corresponding scalar products on projective space (Cauchy formulas), two-point, three-point and more generally cyclic m-point functions are discussed. The three-point function is related to the shape invariant of geodesic triangles in projective space.

24 pages, Ams-Latex, some typos corrected, final version to appear in JGP

References in corpus (4)

• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Coherent states and geodesics: cut locus and conjugate locus
• A remark on Berezin's quantization and cut locus
• Coherent states, line bundles and divisors

Cited by in corpus (10)

• A holomorphic representation of the multidimensional Jacobi algebra
• A holomorphic representation of the Jacobi algebra
• Some remarks on homogeneous Kähler manifolds
• Balanced Metric and Berezin Quantization on the Siegel-Jacobi Ball
• Gaussian distributions, Jacobi group and Siegel-Jacobi space
• Certain circle actions on Kaehler manifolds
• Coherent states and geometry on the Siegel-Jacobi disk
• The Real Jacobi Group Revisited
• Dequantization via quantum channels
• Pullback Coherent States, Squeezed States and Quantization