Symplectic Manifolds, Coherent States and Semiclassical Approximation

Details Symplectic Manifolds, Coherent States and Semiclassical Approximation Symplectic Manifolds, Coherent States and Semiclassical Approximation

1993-10-21

arxiv.org/abs/hep-th/9310138v1

J.Math.Phys.35:2259-2269,1994

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, preprint TCD-4-93, UR-1324,ER40685-774

Scientific paper

10.1063/1.530550

We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using coherent state techniques. These path integrals can be evaluated exactly by semiclassical methods, thus providing examples of localisation formula. Along the way, we also give a local coordinate description for a class of Grassmannians.

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