Universal star products

Abstract

One defines the notion of universal deformation quantization: given any manifold $M$, any Poisson structure $\P$ on $M$ and any torsionfree linear connection $\nabla$ on $M$, a universal deformation quantization associates to this data a star product on $(M,\P )$ given by a series of bidifferential operators whose corresponding tensors are given by universal polynomial expressions in the Poisson tensor $\P$, the curvature tensor $R$ and their covariant iterated derivatives. Such universal deformation quantization exist. We study their unicity at order 3 in the deformation parameter, computing the appropriate universal Poisson cohomology.

To appear in Letters in Mathematical Physics

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• From local to global deformation quantization of Poisson manifolds
• On the Globalization of Kontsevich's Star Product and the Perturbative Poisson Sigma Model

Cited by in corpus (8)

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• Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds
• Quantization of Emergent Gravity
• Tensor calculus on noncommutative spaces
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• The expansion $\star$ mod $\bar{o}({\hslash }^4)$ and computer-assisted proof schemes in the Kontsevich deformation quantization
• Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
• Singular propagators in deformation quantization and Shoikhet-Tsygan formality