LSZ, perturbation and renormalization

[diegzumillo]

My current understanding of renormalization is that the LSZ formula requires normalized fields. So when you normalize them you get some extra parameters from the regularization procedure you encounter along the way. It's an upgrade on my previous understanding of it as some artificial way of hammering out infinities that arise. However, my current understanding also suggests renormalization is unrelated to perturbation theory, but rather stems from incomplete information, so any nonperturbative method should require renormalization or an analogous mechanism that introduces the same number of parameters.

Does that make sense?

 

[diegzumillo]

Since I got an auto-bump, I have been reading about renormalization group and it seems to confirm the basic idea. There's this book called lectures on phase transitions and the renormalization group by Nigel Goldenfeld where he explicitly mentions that RG is essentially non-perturbative. I'm still learning about RG but it seems to be the right thread to start pulling. But I'm not entirely convinced RG and renormalization are exactly the same thing. Certainly related though.

 

[Ian Mitchell]

I don't have a PhD, so take what I say with a grain of salt. But, from what I understand, renormalization is when a loop or something similar arises in a diagram and you need to take out any possible infinities; because any infinity in an actual calculation would make the diagram, and thenceforth the theory non-quantum. So it doesn't really come out of perturbation theory. But it is similar.

The book I'm reading is Introduction to Elementary Particles by Griffiths. It's a really good for a lot of the harder parts of physics.