I have read the renormalization chapters of several QFT books, but I am still highly, deeply confused about some discussion of renormalization conditions and schemes (and some book didn't even offer a discussion, like Peskin & Schroeder.).
The essence of renormalization is to extract experiment prediction from a known result of certain experiment, this can be fully done when we introduced the running coupling. However, is these standard steps contains some physical interpretation?
For me, the philosophy here is: Try one's best to derive a formula of scattering amplitude, which is finite, and input variables of it are all incoming momentum.
If this is true, all physical interpretation of choice of renormalization conditions and schemes may be artificial, the only strandards of these things are: Can they cancel all infinities and give us a formula of scattering amplitude, whose input variables are all incoming momentum.
