Multiple zeta values in deformation quantization

• 成果类型: Article
• 署名作者: Banks, Peter; Panzer, Erik; Pym, Brent
• 署名单位: University of Oxford; University of Edinburgh; McGill University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00970-x
• 发表日期: 2020
• 页码: 79-159
• 关键词: moduli spaces; star product; motives; INTEGRALS; operads; CURVES

摘要

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.