Coherent state embeddings, polar divisors and Cauchy formulas
Differential Geometry
2009-10-31 v2 Mathematical Physics
Algebraic Geometry
math.MP
Quantum Algebra
Symplectic Geometry
Quantum Physics
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.
Cite
@article{arxiv.math/9903105,
title = {Coherent state embeddings, polar divisors and Cauchy formulas},
author = {Stefan Berceanu and Martin Schlichenmaier},
journal= {arXiv preprint arXiv:math/9903105},
year = {2009}
}
Comments
24 pages, Ams-Latex, some typos corrected, final version to appear in JGP