Magnus and Dyson Series for Master Integrals

The Magnus Exponential can be employed to solve the system of differential equations obeyed by Feynman integrals in dimensional regularization. We discuss the basic ideas behind the use of Magnus series expansion, and how the solution naturally arises in terms of repeated integrals that are equivalent to the coefficients of a Dyson series. Finally, we show its application to the evaluation of planar and non-planar two-loop QED vertex diagrams for massive fermions, and to non-planar two-loop integrals contributing to 2 2 scattering of massless particles.