XXV Workshop on Geometric Methods in Physics 2-8.07.2006

Theodore Voronov

Differential forms and odd symplectic geometry

We show that classical differential-geometric objects such as differential forms on a manifold M possess "hidden symmetries" making them objects of odd symplectic geometry. They admit a natural action of the supergroup of all canonical transformations of the anticotangent bundle ΠT*M. The Batalin-Vilkovisky operator (the odd Laplacian on half-densities) from this viewpoint is just the de Rham differential considered with such extra symmetry. An underlying fact is a simple remark from linear algebra concerning the Berezinian of a symplectic transformation.

We discuss this and other relations between classical geometry and odd brackets.

Based on a joint work with H. Khudaverdian.