Feynman graphs. (English) Zbl 1308.81142
Schneider, Carsten (ed.) et al., Computer algebra in quantum field theory. Integration, summation and special functions. Wien: Springer (ISBN 978-3-7091-1615-9/hbk; 978-1-4614-8523-0/ebook). Texts and Monographs in Symbolic Computation, 381-406 (2013).
Summary: In these lectures, I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by multiple polylogarithms. The algebraic properties of multiple polylogarithms are reviewed in the second part of these lectures. The final part of these lectures is devoted to Feynman integrals, which cannot be expressed in terms of multiple polylogarithms. Methods from algebraic geometry provide tools to tackle these integrals.
For the entire collection see [Zbl 1276.81004].
For the entire collection see [Zbl 1276.81004].
MSC:
| 81T18 | Feynman diagrams |
| 81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |
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