Symplectic Manifolds, Coherent States and Semiclassical Approximation

S. G. Rajeev; S. Kalyana Rama; Siddhartha Sen

doi:10.1063/1.530550

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arXiv · hep-th/9310138

Symplectic Manifolds, Coherent States and Semiclassical Approximation

S. G. Rajeev·S. Kalyana Rama·Siddhartha Sen

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Abstract

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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S. G. Rajeev, S. Kalyana Rama, Siddhartha Sen. 1993-10-21. Symplectic Manifolds, Coherent States and Semiclassical Approximation. https://doi.org/10.1063/1.530550

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