English

The deformation quantization of certain super-Poisson brackets and BRST cohomology

Quantum Algebra 2007-05-23 v1 Differential Geometry

Abstract

On every split supermanifold equipped with the Rothstein even 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 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 BRST-cohomology 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).

Keywords

Cite

@article{arxiv.math/0003218,
  title  = {The deformation quantization of certain super-Poisson brackets and BRST cohomology},
  author = {Martin Bordemann},
  journal= {arXiv preprint arXiv:math/0003218},
  year   = {2007}
}

Comments

LATEX 2e, amssymb, latexsym, amsmath, 29 pages, Contribution to the proceedings of the Conf\erence Mosh\e Flato 1999