An Introduction to Motivic Feynman Integrals

被引：3

作者：

Rella, Claudia ^{[1
]}

机构：

[1] Univ Geneva, Sect Math, CH-1211 Geneva, Switzerland

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2021年 / 17卷

关键词：

scattering amplitudes; Feynman diagrams; multiple zeta values; Hodge structures; periods of motives; Galois theory; Tannakian categories; MULTIPLE ZETA VALUES; ALGEBRAIC VARIETY; GALOIS COACTION; ELECTRON G-2; FIELD; SINGULARITIES; AMPLITUDES; RESOLUTION; PERIODS; KNOTS;

D O I：

10.3842/SIGMA.2021.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article gives a short step-by-step introduction to the representation of parametric Feynman integrals in scalar perturbative quantum field theory as periods of motives. The application of motivic Galois theory to the algebro-geometric and categorical structures underlying Feynman graphs is reviewed up to the current state of research. The example of primitive log-divergent Feynman graphs in scalar massless phi(4) quantum field theory is analysed in detail.

引用

页数：56

共 72 条

[1]

Abreu S., 2018, ARXIV180800069

[2] From positive geometries to a coaction on hypergeometric functions [J].