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arXiv · 1812.11649

Multiple zeta values in deformation quantization

Peter Banks·Erik Panzer·Brent Pym
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Abstract

Kontsevich's 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a systematic theory of integration on these moduli spaces via suitable algebras of polylogarithms, and use it to prove that Kontsevich's integrals can be expressed as integer-linear combinations of multiple zeta values. Our proof gives a concrete algorithm for calculating the integrals, which we have used to produce the first software package for the symbolic calculation of Kontsevich's formula.

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Peter Banks, Erik Panzer, Brent Pym. 2018-12-31. Multiple zeta values in deformation quantization. https://doi.org/10.1007/s00222-020-00970-x

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