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Deformation quantization of almost Kähler models and Lagrange-Finsler spaces

J. Math. Phys. 48, 123509 (2007); doi:10.1063/1.2821249

Published 12 December 2007

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Sergiu I. Vacaru
The Fields Institute for Research in Mathematical Science, 222 College Street, Second Floor, Toronto, Ontario M5T 3J1, Canada
Finsler and Lagrange spaces can be equivalently represented as almost Kähler manifolds endowed with a metric compatible canonical distinguished connection structure generalizing the Levi-Civita connection. The goal of this paper is to perform a natural Fedosov-type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental Finsler functions on tangent bundles. ©2007 American Institute of Physics
History: Received 12 July 2007; accepted 13 November 2007; published 12 December 2007
Permalink: http://link.aip.org/link/?JMAPAQ/48/123509/1
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KEYWORDS and PACS

Keywords
PACS
  • 02.40.Hw
    Classical differential geometry
  • 02.30.Sa
    Functional analysis
  • YEAR: 2007

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PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (51)
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  43. We chose a definition of this tensor as in Ref. 6 which is with minus sign compared to the definition used in Ref. 21; we also use a different letter for this tensor, like for the N-connection curvature, because in our case, the symbol N is used for N connections.
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