Hyperlogarithms and periods in Feynman amplitudes

TL;DR

This paper introduces the significance of hyperlogarithms and multiple zeta values in Feynman amplitudes, highlighting their growing importance across mathematics and physics since the 1990s.

Contribution

It offers a concise overview of the rapidly developing role of hyperlogarithms and periods in understanding Feynman amplitudes, connecting diverse scientific fields.

Findings

Hyperlogarithms are crucial in evaluating Feynman integrals.

Multiple zeta values appear naturally in quantum field theory calculations.

The field has seen significant growth since the mid-1990s.

Abstract

The role of hyperlogarithms and multiple zeta values (and their generalizations) in Feynman amplitudes is being gradually recognized since the mid 1990's. The present lecture provides a concise introduction to a fast developing subject that attracts the interests of a wide range of specialists - from number theorists to particle physicists.