Geometrical phases on hermitian symmetric spaces

2004/08/18 by Stefan Berceanu, Berceanu, Stefan · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Geometry and complex manifolds #math-ph #math.DG #math.MP #msc:20C25 #msc:53B35 #msc:81R30

paper · pdf · doi:10.48550/arxiv.math/0408233

LATEX2e, amsfonts, talk at The Sixth International Workshop on Differential Geometry and its Applications and The Third German-Romanian Seminar on Geometry, Babes-Bolyai" University of Cluj-Napoca - Romania, September 1-6, 2003, to appear

arxiv created 2004/08/18 · arxiv updated 2009/12/01

Abstract

For simple Lie groups, the only homogeneous manifolds G/K, where K is maximal compact subgroup,for which the phase of the scalar product of two coherent state vectors is twice the symplectic area of a geodesic triangle are the hermitian symmetric spaces. An explicit calculation of the multiplicative factor on the complex Grassmann manifold and its noncompact dual is presented.It is shown that the multiplicative factor is identical with the two-cocycle considered by A. Guichardet and D. Wigner for simple Lie groups.

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