Partial fractioning reduction of perturbative amplitudes

A new method is presented for the simplification of loop integrals in one particle irreducible diagrams with large numbers of external lines, based on the partial fractioning of products of propagators. Whenever a loop diagram in $d$ dimensions has $d+1$ or more lines that carry the same linear combination of loop momenta, its integral can be reexpressed as a linear combination of integrals with no more than $d+1$ denominators for each such set of lines, of which $d$ are linear in the loop momenta and only one quadratic. In multiloop diagrams, the total number of linear denominators can be reduced further. In integrals with numerator momenta there may also be up to $d+1$ linear factors in the numerator.