Feynman Diagrams and Differential Equations
Abstract
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.
Cite
@article{arxiv.0707.4037,
title = {Feynman Diagrams and Differential Equations},
author = {Mario Argeri and Pierpaolo Mastrolia},
journal= {arXiv preprint arXiv:0707.4037},
year = {2008}
}
Comments
invited review article from Int. J. Mod. Phys. A