Abstract
On every split supermanifold equipped with the Rothstein super-Poisson bracket we construct a deformation quantization by means of a Fedosov-type procedure. In other words, the supercommutative algebra of all smooth sections of the dual Grassmann algebra bundle of an arbitrarily given vector bundle E (equipped with a fiber metric) over a symplectic manifold M will be deformed by a series of bidifferential operators having first order supercommutator proportional to the Rothstein superbracket. Moreover, we discuss two constructions related to the above result, namely the quantized BRST-cohomology for a locally free Hamiltonian Lie group action and the classical BRST cohomology in the general coisotropic (or reducible) case without using a ‘ghosts of ghosts’ scheme.
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Bordemann, M. (2000). The deformation quantization of certain super-Poisson brackets and BRST cohomology. In: Dito, G., Sternheimer, D. (eds) Conférence Moshé Flato 1999. Mathematical Physics Studies, vol 21/22. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1276-3_4
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DOI: https://doi.org/10.1007/978-94-015-1276-3_4
Publisher Name: Springer, Dordrecht
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