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I have been reading about the renormalization of QED. I more or less understand the procedure involving adding the counter terms, calculating the loop corrections using the dimension regularization, and getting the Z coefficients using the $\overline{\textrm{MS}}$ scheme. The textbooks then usually talk about the exact propagators etc. that have all these loop corrections absorbed inside them. The exact photon propagator is then often interpreted as the usual propagator with a correction to the charge and so on.

However, I'm a bit confused about how these exact propagators (and corrected vertices) are then used in real calculations of cross sections in higher orders. Let's for example consider Bhabha scattering to the second order. Some of the 2nd order Feynman diagrams with loops can be "absorbed" into the tree Feynamn diagrams as long as we use the exact propagators. However, there are some diagrams (like the box diagrams) that cannot be absorbed into the tree Feynman diagrams. So how is this calculated in practice? Do people use the exact propagators for higher order corrections?

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  • $\begingroup$ By absorb I mean the fact that if you use the exact propagator for the electron, you don't have to add, for example, a tree level diagram with a photon being emitted and absorbed by the incomming/outgoing electron, since that contribution is already in the exact propagator. $\endgroup$ – lv995 Apr 8 at 14:08

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