The infinite intermediate results are needed because these “infinities” arise from the extrapolation of the low-energy physics to the insanely high energies. However, they have no impact on the low-energy observables. That’s why they’re not a source of problems even in the limit where you treat them as strictly infinite numbers – e.g. when you set \( \epsilon = 0 \) in the dimensional regularization.

— Regularization and renormalization

— Lubos Motl

2011.09.02 Friday ACHK