Wick quantisation of a symplectic manifold

The notion of the Wick star-product is covariantly introduced for a general symplectic manifold equipped with two transverse polarisations. Along the lines of Fedosov method, the explicit procedure is given to construct the Wick symbols on the manifold. The cohomological obstruction is identified to...

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Bibliographic Details
Published in:Nuclear physics. Section B, Proceedings supplement Proceedings supplement, 2001-09, Vol.102, p.144-149
Main Authors: Dolgushev, V.A., Lyakhovich, S.L., Sharapov, A.A.
Format: Article
Language:English
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Summary:The notion of the Wick star-product is covariantly introduced for a general symplectic manifold equipped with two transverse polarisations. Along the lines of Fedosov method, the explicit procedure is given to construct the Wick symbols on the manifold. The cohomological obstruction is identified to the equivalence between the Wick star-product and the Fedosov one. In particular in the Kähler case, the Wick star-product is shown to be equivalent the Weyl one, iff the manifold is a Calabi-Yau one.
ISSN:0920-5632
1873-3832
DOI:10.1016/S0920-5632(01)01549-3