On the Deformation Quantization of super-Poisson Brackets

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.

14 pages, Latex

Cited by in corpus (6)

• Relative formality theorem and quantisation of coisotropic submanifolds
• Wick type deformation quantization of Fedosov manifolds
• Fermionic Ghosts in Moyal String Field Theory
• Star products on graded manifolds and ${\alpha }^{\prime }$-corrections to Courant algebroids from string theory
• Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS Representations, the WKB Expansion, and Applications
• Deformation Theory of Courant Algebroids via the Rothstein Algebra