  It has been known for many years that methods inspired by string theory, such
as the worldline formalism, allow one to write down integral representations
that combine large numbers of Feynman diagrams of different topologies.
However, to make this fact useful for state-of-the-art calculations one has to
confront non-standard integration problems where neither the known integration
techniques for Feynman diagrams nor algebraic manipulation programs are of much
help. Here I will give a progress report on this long-term project focussing on
photon amplitudes at one and two loops, in vacuum and in external fields.
