Kontsevich's Universal Formula for Deformation Quantization and the Campbell-Baker-Hausdorff Formula, I

Vinay Kathotia

Kontsevich's Universal Formula for Deformation Quantization and the Campbell-Baker-Hausdorff Formula, I

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arxiv math/9811174 v2 pith:XVATGDNA submitted 1998-11-30 math.QA math-phmath.MP

Kontsevich's Universal Formula for Deformation Quantization and the Campbell-Baker-Hausdorff Formula, I

Vinay Kathotia This is my paper

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keywords formuladeformationuniversalcampbell-baker-hausdorffkontsevichpoissonquantizationarbitrary

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We relate a universal formula for the deformation quantization of arbitrary Poisson structures proposed by Maxim Kontsevich to the Campbell-Baker-Hausdorff formula. Our basic thesis is that exponentiating a suitable deformation of the Poisson structure provides a prototype for such universal formulae.

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A path integral on the Hilbert space of a Lie group is built by decompactifying to the Lie algebra and summing over winding sectors in maximal tori, yielding two-loop heat-kernel coefficients for Euler-Arnold systems.