Abstract
The relationship between coherent states and geodesics is emphasized. It is found that CL 0 = Σ0, where CL 0 is the cut locus of 0 and Σ0 is the locus of coherent vectors othogonal to 0 >. The result is proved for manifolds on which the exponential from the Lie algebra to the Lie group equals the geodesic exponential. The conjugate loci on hermitian symmetric spaces are analyzed also in the context of the coherent state approach. The results are illustrated on the complex Grassmann manifold.
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Berceanu, S. (1995). Coherent States and Global Differential Geometry. In: Antoine, JP., Ali, S.T., Lisiecki, W., Mladenov, I.M., Odzijewicz, A. (eds) Quantization, Coherent States, and Complex Structures. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1060-8_15
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DOI: https://doi.org/10.1007/978-1-4899-1060-8_15
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