Multiple zeta values in deformation quantization

Peter Banks; Erik Panzer; Brent Pym

Multiple zeta values in deformation quantization

Peter Banks, Erik Panzer, Brent Pym

School of Mathematics

Research output: Working paper

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.

Original language	English
Publisher	ArXiv
Pages	1-71
Number of pages	71
Publication status	Published - 31 Dec 2018

Keywords

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

Access to Document

1812.11649v1Submitted manuscript, 908 KB

https://arxiv.org/abs/1812.11649

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