Multiple zeta values in deformation quantization

被引：11

作者：

Banks, Peter ^{[1
]}

Panzer, Erik ^{[1
]}

Pym, Brent ^{[2
,3
]}

机构：

[1] Univ Oxford, Oxford, England

[2] Univ Edinburgh, Edinburgh, Midlothian, Scotland

[3] McGill Univ, Montreal, PQ, Canada

来源：

INVENTIONES MATHEMATICAE | 2020年 / 222卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

11M32; 14H10; 53D55; 81Q30; MODULI SPACES; STAR PRODUCT; MOTIVES; INTEGRALS; OPERADS; CURVES;

D O I：

10.1007/s00222-020-00970-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：79 / 159

页数：81

共 65 条

[1] Logarithms and deformation quantization [J].