FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS

Feynman Diagrams and Differential Equations

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of oneand two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less triv...

Scattering equations and Feynman diagrams

We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in φ3-theory. We also discuss the generalization to general scalar field theories with φp interactions, corresponding to polygonal graphs ...

Differential Equations for Feynman Graph Amplitudes

It is by now well established that, by means of the integration by part identities [1], all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is shown in this paper that the integration by part identities can be further used for obtaining a linear system of first order differential equations for the...

Evaluating multiloop Feynman integrals by differential equations

One year ago Henn suggested a new approach to solve differential equations for multiloop Feyn-man integrals. It is based on the notion of uniform transcendentality. A brief review of applications of this approach is presented.

Feynman diagrams versus Fermi-gas Feynman emulator