Multiple zeta values in deformation quantization

Peter Banks, Erik Panzer, Brent Pym

Research output: Working paper


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.
Original languageEnglish
Number of pages71
Publication statusPublished - 31 Dec 2018


  • math.QA
  • hep-th
  • math-ph
  • math.AG
  • math.MP
  • math.NT

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