Laplacians in odd symplectic geometry. (English) Zbl 1047.53049

Khudaverdian, Hovhannes M.

Voronov, Theodore (ed.), Quantization, Poisson brackets and beyond. London Mathematical Society regional meeting and workshop on quantization, deformations, and new homological and categorical methods in mathematical physics, Manchester, UK, July 6–13, 2001. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3201-8). Contemp. Math. 315, 199-212 (2002).

Author’s summary: “We consider odd Laplace operators arising in odd symplectic geometry. An 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 Lagragian 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.”
For the entire collection see [Zbl 1007.53002].

Reviewer: David Iglesias-Ponte (University Park)

MSC:

53D05	Symplectic manifolds (general theory)
58J60	Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
58A50	Supermanifolds and graded manifolds
53D17	Poisson manifolds; Poisson groupoids and algebroids
81T70	Quantization in field theory; cohomological methods

Keywords:

symplectic geometry; Laplace operators; supermanifolds