Abstract
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 ζ 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.
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Duhr, C. Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes. J. High Energ. Phys. 2012, 43 (2012). https://doi.org/10.1007/JHEP08(2012)043
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DOI: https://doi.org/10.1007/JHEP08(2012)043