Symplectic geometries on supermanifolds
High Energy Physics - Theory
2008-11-26 v3
Abstract
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of symplectic geometries on supermanifolds.
Cite
@article{arxiv.0708.3778,
title = {Symplectic geometries on supermanifolds},
author = {P. M. Lavrov and O. V. Radchenko},
journal= {arXiv preprint arXiv:0708.3778},
year = {2008}
}
Comments
LaTex, 1o pages, LaTex, changed content