Algebraic reduction of one-loop Feynman graph amplitudes. (English) Zbl 0956.81054
Summary: An algorithm for the reduction of one-loop \(n\)-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension [A. I. Davydychev (1991)]and reduce these by recurrence relations to integrals in generic dimension [O. V. Tarasov (1996)]. Also the integration-by-parts method [F. V. Tkachov (1981); K. G. Chetyrkin, F. V. Tkachov (1981)]is used to reduce indices (powers of scalar propagators) of the scalar diagrams. The obtained recurrence relations for one-loop integrals are explicitly evaluated for 5- and 6-point functions. In the latter case the corresponding Gram determinant vanishes identically for \(d=4\), which greatly simplifies the application of the recurrence relations.
MSC:
| 81T18 | Feynman diagrams |
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