Coherent states and geodesics: cut locus and conjugate locus

Details Coherent states and geodesics: cut locus and conjugate locus Coherent states and geodesics: cut locus and conjugate locus

1995-02-22

arxiv.org/abs/dg-ga/9502007v2

J. Geom. Phys. 21 (1997) 149-168

Mathematics

Differential Geometry

19 pages, enlarged version, 14 pages, Latex + some macros from Revtex + some AMS fonts

Scientific paper

10.1016/S0393-0440(96)00011-3

The intimate relationship between coherent states and geodesics is pointed out. For homogenous manifolds on which the exponential from the Lie algebra to the Lie group equals the geodesic exponential, and in particular for symmetric spaces, it is proved that the cut locus of the point $0$ is equal to the set of coherent vectors orthogonal to $\vert 0>$. A simple method to calculate the conjugate locus in Hermitian symmetric spaces with significance in the coherent state approach is presented. The results are illustrated on the complex Grassmann manifold.

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