Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds

Details Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds

2009-10-02

arxiv.org/abs/0910.0459v1

AIP Conf.Proc.1200:204-214,2010

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, no figures. Invited talk at the 17th International Conference on Supersymmetry and the Unification of Fundamental In

Scientific paper

10.1063/1.3327559

After a brief description of the $\mathbb{Z}$-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter $\hbar$, in the case of symplectic manifolds. The graded differential Poisson algebra endows the manifold with a connection, not necessarily torsion-free, and places upon the connection various constraints.

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