Calculation of many-loop diagrams of perturbation theory

Some identities are formulated for semi-unique vertices and semi-unique triangles that occur in the diagrams of perturbation theory with massless scalar particles. The use of these identities makes it possible to develop a reduction scheme by means of which the result can be obtained for many-loop diagrams without expansion in infinite series in Gegenbauer polynomials and without the use of the operation of differentiation, which leads to additional kinematic complications. As a result, the calculation of many-loop diagrams of the perturbation theory is significantly simplified.