Algebraic algorithms for multiloop calculations. The first 15 years. What's next?
Fyodor V. Tkachov
Abstract
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the corresponding Feynman-parametrized integrands into a form that is optimal for numerical integration, with all the poles in D-4 explicitly extracted.
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