Laplacians in Odd Symplectic Geometry
نویسنده
چکیده
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.
منابع مشابه
Differential Forms and Odd Symplectic Geometry
We remind the main facts about the odd Laplacian acting on half-densities on an odd symplectic manifold and discuss a homological interpretation for it suggested recently by P. Ševera. We study relations of odd symplectic geometry with classical objects. We show that the Berezinian of a canonical transformation for an odd symplectic form is a polynomial in matrix entries and a complete square. ...
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