Algebraic algorithms for multiloop calculations. The first 15 years. What's next?

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.

5 pages, PS; 7-11-98: maintenance (PS, misprints, etc.)

References in corpus (3)

• Connection between Feynman integrals having different values of the space-time dimension
• Euclidean asymptotic expansions of Green functions of quantum fields (I) Expansions of products of singular functions
• Explicit solutions of the n--loop vacuum integral recurrence relations

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