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Hochschild cohomology of the Weyl algebra and traces in deformation quantization

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arxiv math/0311303 v2 pith:OHZ5BCUJ submitted 2003-11-18 math.QA

Boris Feigin (Landau Institute) , Giovanni Felder (ETH Zurich) , Boris Shoikhet (ETH Zurich) This is my paper · ORCID
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keywords algebracohomologydeformationformulahochschildquantizationweylcanonical
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We give a formula for a cocycle generating the Hochschild cohomology of the Weyl algebra with coefficients in its dual.It is given by an integral over the configuration space of ordered points on a circle. Using this formula and a non-commutative version of formal geometry, we obtain an explicit expression for the canonical trace in deformation quantization of symplectic manifolds.

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  1. Scalar Field on a higher-spin Background via Fedosov quantization

    hep-th 2024-12 conditional novelty 6.0 of 10

    A Fedosov-quantized Wigner function and the Feigin-Felder-Shoikhet trace yield a manifestly covariant action for scalar matter coupled to conformal higher-spin backgrounds.

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