Coherent state embeddings, polar divisors and Cauchy formulas

Details Coherent state embeddings, polar divisors and Cauchy formulas Coherent state embeddings, polar divisors and Cauchy formulas

1999-03-17

arxiv.org/abs/math/9903105v2

Mathematics

Differential Geometry

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

Scientific paper

10.1016/S0393-0440(99)00075-3

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.

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