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Renormalization is a beautiful hack, but it is a hack. Let's take infinity, subtract other infinitites add a bit of alchemy and here is our prediction. <- from
by ternaus 6y ago
Renormalization is a beautiful hack, but it is a hack.
Let's take infinity, subtract other infinitites add a bit of alchemy and here is our prediction. <- from mathematical perspective this is a very sketchy business.
But it works. And it works in other fields. For example in the theory of phase transitions (I have PhD on the topic :))
And it is pretty common in Physics to work with sketchy constructions for decades before mathematicians catch up.
I love the example of "Generalized Functions" (examples are Delta function and Step Function) that were widely in Physics decades before a consistent mathematical theory was developed.
I hope, at some point we will have a similar story with Renormalization theory.
- improbable22 6y agoWell, that's how this was discovered, as a clever hack that worked. In the 1940s. But it was subsequently understood much better, in the 70s. There are no infinities involved in thinking about renormalisation group flow. That progress seems like exactly the story the article is trying to tell. It's indeed not so different from the story of calculus. You don't even need Dirac, the very basic idea of calculus is a hack for dividing zero by zero without getting confused, which later got nicely cleaned up to became respectable mathematics.
- ssivark 6y agoHey, I think we’ve had a good understanding of renormalization group for at least a couple of decades! It might have been considered a hack before that, but I think by now we appreciate exactly what role it plays, and how to exploit it to the best of our abilities (Eg: effective field theories). See my other top-level comment for an interpretation. Btw, what was your thesis on? :-) PS: My thesis also touched on some of these ideas, but from the hep-th side.