Multiple zeta values in deformation quantization

Autor:	Banks, Peter, Panzer, Erik, Pym, Brent
Rok vydání:	2018
Předmět:	Mathematics - Quantum Algebra High Energy Physics - Theory Mathematical Physics Mathematics - Algebraic Geometry Mathematics - Number Theory
Zdroj:	Inventiones mathematicae 222 (2020), pp. 79-159
Druh dokumentu:	Working Paper
DOI:	10.1007/s00222-020-00970-x
Popis:	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. Comment: 71 pages; software available at http://bitbucket.org/bpym/starproducts/ and https://bitbucket.org/PanzerErik/kontsevint/
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1812.11649 Zobrazit plný text záznamu View this record from Arxiv