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Coherent States and Global Differential Geometry

In: Quantization, Coherent States, and Complex Structures

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  • Stefan Berceanu

    (CNRS - Université Paris 7-Denis Diderot, Equipe de Physique Mathématique et Géométrie Institut de Mathématique
    Institute of Atomic Physics Institute of Physics and Nuclear Engineering, Department of Theoretical Physics)

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.

Suggested Citation

  • Stefan Berceanu, 1995. "Coherent States and Global Differential Geometry," Springer Books, in: J.-P. Antoine & S. Twareque Ali & W. Lisiecki & I. M. Mladenov & A. Odzijewicz (ed.), Quantization, Coherent States, and Complex Structures, pages 131-140, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1060-8_15
    DOI: 10.1007/978-1-4899-1060-8_15
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