相干态嵌入、极除子和柯西公式
Coherent state embeddings, polar divisors and Cauchy formulas
摘要：
对于任意可量化的紧致Kaehler流形，研究了基于流形的相干态给出的几何与通过相干态映射到射影空间实现的代数（射影）几何之间的关系.讨论了极除子、流形上相干向量的标量积与射影空间上相应的标量积的关系式（柯西公式）、两点、三点以及更一般的循环m-点函数。三点函数与射影空间中测地三角形的形状不变量有关。
英文摘要：
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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