Khudaverdian, Hovhannes M. and Voronov, Theodore
(2002)
*On odd Laplace operators.*
Letters in Mathematical Physics, 62 (2).
pp. 127-142.
ISSN 1573-0530

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## Abstract

Abstract We consider odd Laplace operators acting on densities of various weights on an odd Poisson (= Schouten) manifold M. We prove that the case of densities of weight 1/2 (half-densities) is distinguished by the existence of a unique odd Laplace operator depending only on a point of an 'orbit space' of volume forms. This includes earlier results for the odd symplectic case, where there is a canonical odd Laplacian on half-densities. The space of volume forms on M is partitioned into orbits by the action of a natural groupoid whose arrows correspond to the solutions of the quantum Batalinâ€“Vilkovisky equations. We compare this situation with that of Riemannian and even Poisson manifolds. In particular, we show that the square of an odd Laplace operator is a Poisson vector field defining an analog of Weinstein's 'modular class'.

Item Type: | Article |
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Uncontrolled Keywords: | groupoids - half-densities - Laplacians - modular class - odd Poisson geometry - odd Laplace operators - quantum master equation |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds MSC 2010, the AMS's Mathematics Subject Classification > 81 Quantum theory |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 14 Aug 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/487 |

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