The Hopf algebra structure of multiple harmonic sums

Abstract

Multiple harmonic sums appear in the perturbative computation of various quantities of interest in quantum field theory. In this article we introduce a class of Hopf algebras that describe the structure of such sums, and develop some of their properties that can be exploited in calculations.

Talk for Loops & Legs in QFT, Zinnowitz, 2004

References in corpus (4)

• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity

Cited by in corpus (5)

• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Quasi-shuffle products revisited
• Shuffle relations for regularised integrals of symbols
• Finite and Symmetric Euler Sums and Finite and Symmetric (Alternating) Multiple $T$-Values