Laplacians in Odd Symplectic Geometry
Differential Geometry
2007-05-23 v1 High Energy Physics - Theory
Abstract
We consider odd Laplace operators arising in odd symplectic geometry. Approach based on semidensities (densities of weight 1/2) is developed. The role of semidensities in the Batalin--Vilkovisky formalism is explained. In particular, we study the relations between semidensities on an odd symplectic supermanifold and differential forms on a purely even Lagrangian submanifold. We establish a criterion of ``normality'' of a volume form on an odd symplectic supermanifold in terms of the canonical odd Laplacian acting on semidensities.
Cite
@article{arxiv.math/0212354,
title = {Laplacians in Odd Symplectic Geometry},
author = {Hovhannes M. Khudaverdian},
journal= {arXiv preprint arXiv:math/0212354},
year = {2007}
}
Comments
LaTeX2e, 19 pages