[pfedor]

What's "true" physics and what's just a computational technique is a distinction which seems rather philosophical, and I don't mean it as a positive thing.

In any case, there's more to Feynman diagrams than your comment implies. For example, think of the optical theorem. You can take a diagram with a loop in the middle and cut it in half, and get two diagrams of a lower order, say originally you had A + B -> C + D and you get A + B -> X and X -> C + D (where X can be any number of particles), and the amplitude for the former is the integral over all momenta of the amplitudes for the sequence of the latter. What it means is you can think of a "true" physical sequence of events, A + B -> X followed by X -> C + D, which contributes to the cross-section for A + B -> C + D and the math behind it is the same as used for the A + B -> C + D scattering with a not-"true" X (i.e., X with non-physical momenta) in the middle of the Feynman diagram.