CONNECTION BETWEEN FEYNMAN-INTEGRALS HAVING DIFFERENT VALUES OF THE SPACE-TIME DIMENSION

A systematic algorithm for obtaining recurrence relations for dimensio nally regularized Feynman integrals with respect to the space-time dim ension d is proposed. The relation between d- and (d-2)-dimensional in tegrals is given in terms of a differential operator for which an expl icit formula can be obtained for each Feynman diagram. We show how the method works for one-, two-, and three-loop integrals. The new recurr ence relations with respect to d are complementary to the recurrence r elations which derive from the method of integration by parts. We find that the problem of the irreducible numerators in Feynman integrals c an be naturally solved in the framework of the proposed generalized re currence relations.