Feynman Diagrams and Differential Equations

Details Feynman Diagrams and Differential Equations Feynman Diagrams and Differential Equations

2007-07-27

arxiv.org/abs/0707.4037v1

Int.J.Mod.Phys.A22:4375-4436,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

invited review article from Int. J. Mod. Phys. A

Scientific paper

10.1142/S0217751X07037147

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 one- and 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 trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D=4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.

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