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On the Deformation Quantization of super-Poisson Brackets

Martin Bordemann
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Abstract

We show that for every vector bundle E over any given symplectic manifold M there exists an explicitly given super-Poisson bracket on the space of sections of the dual Grassmann bundle associated to E built out of symplectic structure of M, a fibre metric on E, and a connection in E compatible with the given fibre metric. Moreover, we construct a deformation quantization for this space of sections by means of a Fedosov type procedure.

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Martin Bordemann. 1996-05-24. On the Deformation Quantization of super-Poisson Brackets. https://arxiv.org/abs/q-alg/9605038

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