Multiple zeta values in deformation quantization
Quantum Algebra
2020-09-07 v1 High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
math.MP
Number Theory
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.
Keywords
Cite
@article{arxiv.1812.11649,
title = {Multiple zeta values in deformation quantization},
author = {Peter Banks and Erik Panzer and Brent Pym},
journal= {arXiv preprint arXiv:1812.11649},
year = {2020}
}
Comments
71 pages; software available at http://bitbucket.org/bpym/starproducts/ and https://bitbucket.org/PanzerErik/kontsevint/