The deformation quantization of certain superPoisson brackets and BRST cohomology
Abstract
On every split supermanifold equipped with the Rothstein even superPoisson bracket we construct a deformation quantization by means of a Fedosovtype 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 fibre 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 BRSTcohomology for a locally free Hamiltonian Lie group action (together with H.C.Herbig and S.Waldmann) and the classical BRST cohomology in the general coistropic (or reducible) case without using a `ghosts of ghosts' scheme (together with H.C.Herbig).
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2000
 DOI:
 10.48550/arXiv.math/0003218
 arXiv:
 arXiv:math/0003218
 Bibcode:
 2000math......3218B
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Differential Geometry;
 16S80;
 58C50;
 81Q60;
 81S99
 EPrint:
 LATEX 2e, amssymb, latexsym, amsmath, 29 pages, Contribution to the proceedings of the Conf\erence Mosh\e Flato 1999