Deformation quantization with traces

Abstract

In the present paper we prove a statement closely related to the cyclic formality conjecture. In particular, we prove that for a divergence-free Poisson bivector field on R^d, the Kontsevich star-product with the harmonic angle function is cyclic. We also prove a globalization of this theorem in the case of arbitrary Poisson manifolds and prove a generalization of the Connes-Flato-Sternheimer conjecture on closed star-products in the Poisson case.

14 pages, 2 figures. Discussion of general volume forms corrected

References in corpus (1)

• A path integral approach to the Kontsevich quantization formula

Cited by in corpus (30)

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• Noncommutative $R^d$ via closed star product
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• Quantum mechanics with coordinate dependent noncommutativity
• Formality theorems for Hochschild chains in the Lie algebroid setting
• Effective Batalin--Vilkovisky theories, equivariant configuration spaces and cyclic chains
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• Diffeomorphism covariant star products and noncommutative gravity
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
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• Quantization of Emergent Gravity
• SL(2,C) gravity on noncommutative space with Poisson structure
• Traces for star products on the dual of a Lie algebra
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• Deformation Quantization of Poisson Structures Associated to Lie Algebroids
• Tensor calculus on noncommutative spaces
• Weak associativity and deformation quantization
• U(2,2) gravity on noncommutative space with symplectic structure
• Gravity algebra structure on the negative cyclic homology of Calabi-Yau algebras
• Conserved symmetries in noncommutative quantum mechanics
• On the inverse mapping of the formal symplectic groupoid of a deformation quantization
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• Discrete Wigner-Weyl calculus for the finite lattice