TL;DR
The paper introduces new functional equations relating Feynman integrals with different invariants and masses, providing a method for their derivation and applications in analytic continuation across kinematic domains.
Contribution
It presents novel functional equations for Feynman integrals and a systematic method to derive them, enhancing understanding of their relationships and analytic properties.
Findings
Functional equations connect integrals with different parameters.
Decomposition of propagator integrals into simpler forms.
Application of equations for analytic continuation.
Abstract
New types of relationships between Feynman integrals are presented. It is shown that Feynman integrals satisfy functional equations connecting integrals with different values of scalar invariants and masses. A method is proposed for obtaining such relations. The derivation of functional equations for one-loop propagator- 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 scalar invariants and one propagator massless. The vertex - type integral can be written as a sum over vertex integrals with all but one propagator massless and one external momenta squared equal to zero. It is demonstrated that the functional equations can be used for the analytic continuation of Feynman integrals to different kinematic domains.
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