Polylogarithms and multizeta values in massless feynman amplitudes

Abstract

The last two decades have seen a remarkable development of analytic methods in the study of Feynman amplitudes in perturbative quantum field theory. The present lecture offers a physicists’ oriented survey of Francis Brown’s work on singlevalued multiple polylogarithms, the associated multizeta periods and their application to Schnetz’s graphical functions and to x-space renormalization. To keep the discussion concrete we restrict attention to explicit examples of primitively divergent graphs in a massless scalar QFT.