Coherent states, phases and symplectic areas of geodesic triangles

Details Coherent states, phases and symplectic areas of geodesic triangles Coherent states, phases and symplectic areas of geodesic triangles

1999-03-31

arxiv.org/abs/math/9903190v1

"Coherent States, Quantization and Gravity", Edited by M. Schlichenmaier, S.T. Ali, A. Strasburger, A.Odzijewicz, Proceedings

Mathematics

Differential Geometry

8 pages, Latex2e, AMS fonts, to appear in "Coherent States, Quantization and Gravity", Edited by M. Schlichenmaier, S. T. Ali,

Scientific paper

On certain manifolds, the phase which appears in the scalar product of two coherent state vectors is twice the symplectic area of the geodesic triangle determined by the corresponding points on the manifold and the origin of the system of coordinates. This result is proved for compact Hermitian symmetric spaces using the generalization via coherent states of the shape invariant for geodesic triangles and re-obtained on the complex Grassmannian by brute- force calculation.

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