A Star Product for Differential Forms on Symplectic Manifolds

Abstract

We present a star product between differential forms to second order in the deformation parameter $\hslash$. The star product obtained is consistent with a graded differential Poisson algebra structure on a symplectic manifold. The form of the graded differential Poisson algebra requires the introduction of a connection with torsion on the manifold, and places various constraints upon it. The star product is given to second order in ${\hslash }^2$.

25 pages, no figures, revtex4. Section included on changing coordinates, slight change in notation, and S. McCurdy and B. Zumino have removed their names

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• Noncommutative Differential Calculus for D-brane in Non-Constant B Field Background
• Poisson Algebra of Differential Forms

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• Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
• Action principles for higher and fractional spin gravities
• Gauge field theories with covariant star-product
• Integrable Hopf twists, marginal deformations and generalised geometry
• Differential Poisson Sigma Models with Extended Supersymmetry
• Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
• Quantum Space-Time and Noncommutative Gauge Field Theories