Bogner, Christian; Brown, Francis Feynman integrals and iterated integrals on moduli spaces of curves of genus zero. (English) Zbl 1316.81040 Commun. Number Theory Phys. 9, No. 1, 189-238 (2015). This paper continues some work of Francis Brown from IHES in Bures-sur-Yvette on iterated integrals in quantum field theory, multiple zeta values, periods of moduli spaces and certain Feynman integrals. The main goal of the present paper is to provide effective algorithms for a symbolic computation of integrals on n-dimensional moduli spaces. It is suggested to integrate out each single variable at a time using the algebra of iterated symbolic integrals. The main goal is to apply this method of calculation to a large class of Feynman amplitudes. Actually, there are two possible approaches. One is referred to by Brown as the method of hyperlogarithms. It involves Schwinger parameters. The other, which he now describes, makes a more systematic use of the geometry of moduli spaces. Focusing on applications the method may hopefully be useful in the following situations: (1) Feynman graphs with several masses, (2) gauge theory, (3) ultra-violet divergences compatible with the BPHZ renormalization procedure. It may very well be that the method is suited for automatic calculations on a computer. Reviewer: Gert Roepstorff (Aachen) Cited in 25 Documents MSC: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) 14H10 Families, moduli of curves (algebraic) 68W30 Symbolic computation and algebraic computation Keywords:Feynman integrals; iterated integrals in QED; multiple zeta values; periods of moduli spaces; symbolic computation; hyperlogarithms Software:HarmonicSums; Hypexp; HYPERDIRE; XSummer; HPL; FeynEdit; Nestedsums PDFBibTeX XMLCite \textit{C. Bogner} and \textit{F. Brown}, Commun. Number Theory Phys. 9, No. 1, 189--238 (2015; Zbl 1316.81040) Full Text: DOI arXiv