2002/12/27 by Hovhannes M. Khudaverdian
Mathematics · Physics and Astronomy · #math.DG #hep-th #msc:53D05 #msc:58A50
published as Contemp.Math. 315 (2002) 199-212 · LaTeX2e, 19 pages
arxiv created 2002/12/27 · arxiv updated 2009/11/30
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.