Algebraic reduction of one-loop Feynman graph amplitudes

An algorithm for the reduction of one-loop n-point tensor integrals to basi c integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension [A.I. Davydychev, Phys. Lett. B 263 (1991) 107] and reduce these by recurrence relations to integrals in generic dimension [O.V . Tarasov, Phys. Rev. D 54 (1996) 6479]. Also the integration-by-parts meth od [F.V. Tkachov, Phys. Lett. B 100 (1981) 65; K.G. Chetyrkin, F.V. Tkachov , Nucl. Phys. B 192(1981) 159] 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. i n the latter case the corresponding Gram determinant vanishes identically f or d = 4, which greatly simplifies the application of the recurrence relati ons. (C) 2000 Elsevier Science B.V. All rights reserved.