Abstract:
A method of calculating massless Feynman integrals on the basis of
a “uniqueness” relation is developed and applications are
discussed. The method involves several algebraic steps but not the
calculation of integrals of elementary or special functions or
expansion in infinite series and summation of them. The simplicity
and effectiveness of the method are illustrated by the calculation
of two- and three-loop dimensionally regularized integrals. The
technique is applied to the analytic calculation of the last
diagrams that complete the five-loop renormalization-group
calculations in the $\varphi^4$ theory.
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