Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic Manifolds, Coherent States and Semiclassical Approximation   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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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph