This article is cited in 2 papers

Deformation quantization of framed presymplectic manifolds

N. D. Gorev, B. M. Elfimov, A. A. Sharapov

Tomsk State University, Tomsk, Russia

Abstract: We consider the problem of deformation quantization of presymplectic manifolds in the framework of the Fedosov method. A class of special presymplectic manifolds is distinguished for which such a quantization can always be constructed. We show that in the general case, the obstructions to quantization can be identified with some special elements of the third cohomology group of a differential ideal associated with the presymplectic structure.

Keywords: presymplectic manifold, deformation quantization, Fedosov quantization.

PACS: 03.65.Ca

MSC: 53D55

Received: 15.03.2020
Revised: 15.03.2020

DOI: 10.4213/tmf9907

 English version: Theoretical and Mathematical Physics, 2020, 204:2, 1079–1092

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