Coherent states and geodesics: cut locus and conjugate locus

✍ Scribed by S Berceanu

• Book ID: 104343381
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 994 KB
• Volume: 21
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(96)00011-3

✦ Synopsis

The intimate relationship between coherent states and geodesics is pointed out. For homogenous manifolds in 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 IO). A simple method to calculate the conjugate locus in Hetmitian symmetric spaces with significance in the coherent state approach is presented. The results are illustrated on the complex Grassmannian manifold.