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.

中文翻译：

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变形量化中的多个zeta值

Kontsevich 1997 年的泊松括号变形量化公式是费曼展开式，涉及标记圆盘模空间上的体积积分。我们通过合适的多对数代数在这些模空间上开发了一个系统的积分理论，并用它来证明 Kontsevich 的积分可以表示为多个 zeta 值的整数线性组合。我们的证明给出了计算积分的具体算法，我们用它来生成第一个用于 Kontsevich 公式符号计算的软件包。