Titlebook: Computer Algebra in Quantum Field Theory; Integration, Summati Carsten Schneider,Johannes Blümlein Book 2013 Springer-Verlag Wien 2013 Diff

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Simplifying Multiple Sums in Difference Fields,c number identities extending those from Paule and Schneider, 2003. In addition, the newly developed package . is introduced that combines the presented tools. In this way, large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be solved completely automatically.

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Kyoichi Kijima,Junichi Iijima,Bumpei Nakanol weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound ..

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Capturing Knowledge of the Systemw the Hopf algebra of polynomials carries a refined renormalization group property, implying its coarser form on the level of correlation functions. Application to scalar quantum field theory reveals the scaling behaviour of individual Feynman graphs.

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Harmonic Sums, Polylogarithms,Special Numbers, and Their Generalizations,l weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound ..

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