Geodesic
Quantization of symplectic manifolds with conical points
Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 3, pp. 374-387 Cet article a éte moissonné depuis la source Math-Net.Ru

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Quantization of a general nonlinear phase manifold $\mathfrak X$ in the quasicIassical approximation leads to the two-dimensional analog of the Bohr–Sommerfeld conditions, in which the form $pdq$ is replaced by $dp\Lambda dq$ and the vacuum energy $h/2$ by $h\nu/2$, where $\nu$ is the index of two-dimensional noncontractable cycles in $\mathfrak X$ . A study is made of smooth manifolds $\mathfrak X$ on which the index $\nu$ is integral and manifolds with conical singularities, on which $\nu$ can take half-integral values. Smooth functions $f$ on $\mathfrak X$ are associated with operators $\hat{f}$ that act on the sections of a ertain sheaf and locally have the form $\hat{f}=f(q,-ih\partial/\partial q)$, $h\to0$. 
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     author = {M. V. Karasev and V. P. Maslov},
     title = {Quantization of symplectic manifolds with conical points},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {374--387},
     year = {1982},
     volume = {53},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_53_3_a4/}
}
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M. V. Karasev; V. P. Maslov. Quantization of symplectic manifolds with conical points. Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 3, pp. 374-387. http://geodesic.mathdoc.fr/item/TMF_1982_53_3_a4/

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