Mathematics – Symplectic Geometry
Scientific paper
2002-03-12
Quantization, Poisson Brackets and Beyond, Theodore Voronov (ed.), Contemp. Math., Vol. 315, Amer. Math. Soc., Providence, RI,
Mathematics
Symplectic Geometry
17 pages; to appear in the proceedings of the Conference on Quantization, Deformations and New Homological and Categorical Met
Scientific paper
This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles (E\to M_{0}) by canonically associating to such a bundle a graded symplectic supermanifold ((M,\Omega)), with (\textrm{deg}(\Omega)=2). Conversely, every such manifold arises in this way. We describe the algebra of functions on (M) in terms of (E) and show that ``BRST charges'' on (M) correspond to Courant algebroid structures on (E), thereby constructing the standard complex for the latter as a generalization of the classical BRST complex. As an application of these ideas, we prove the acyclicity of ``higher de Rham complexes'', a generalization of a classic result of Fr\"{o}hlicher-Nijenhuis, and derive several easy but useful corollaries.
No associations
LandOfFree
On the structure of graded symplectic supermanifolds and Courant algebroids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the structure of graded symplectic supermanifolds and Courant algebroids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the structure of graded symplectic supermanifolds and Courant algebroids will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-263210