Geometry of Generalized Coherent States : Some Calculations of Chern Characters

Details Geometry of Generalized Coherent States : Some Calculations of Chern Characters Geometry of Generalized Coherent States : Some Calculations of Chern Characters

2001-09-28

arxiv.org/abs/hep-th/0109215v1

Physics

High Energy Physics

High Energy Physics - Theory

Latex File, 1+22 pages

Scientific paper

This is a continuation of the preceding paper (hep-ph/0108219). First of all we make a brief review of generalized coherent states based on Lie algebra su(1,1) and prove that the resolution of unity can be obtained by the curvature form of some bundle. Next for a set of generalized coherent states we define a universal bundle over the infinite-dimensional Grassmann manifold and construct the pull-back bundle making use of a projector from the parameter space to this Grassmann one. We mainly study Chern characters of these bundles. Although the Chern characters in the infinite-dimensional case are in general not easy to calculate, we can perform them for the special cases. In this paper we report our calculations and propose some problems.

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