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Abstract: New types of relationships between Feynman integrals are presented. It isshown that Feynman integrals satisfy functional equations connecting integralswith different values of scalar invariants and masses. A method is proposed forobtaining such relations. The derivation of functional equations for one-looppropagator- and vertex - type integrals is given. It is shown that a propagator- type integral can be written as a sum of two integrals with modified scalarinvariants and one propagator massless. The vertex - type integral can bewritten as a sum over vertex integrals with all but one propagator massless andone external momenta squared equal to zero. It is demonstrated that thefunctional equations can be used for the analytic continuation of Feynmanintegrals to different kinematic domains.

Autor: O. V. Tarasov


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