1203.0454 (Claude Duhr)

Hopf algebras, coproducts and symbols: an application to Higgs boson
amplitudes    [PDF]

Claude Duhr

We show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values. We illustrate our approach by rewriting the two-loop helicity amplitudes for a Higgs boson plus three gluons in a simplified and compact form involving only classical polylogarithms.

View original: http://arxiv.org/abs/1203.0454