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I learned that renormalization used in the standard model while working is using some math that has not yet been proved. Put very simple renormalization is subtracting an infinite number from another infinite number to get a finite number. I learned during a lecture on quantum field theory that there is no mathematical proof yet for some of the mathematics used in renormalization of the standard model. However the experiment show it works. So it's sort of math empirically confirmed?

My question now is what are the exact things with renormalization that are not yet proved mathematically? Could you guide me towards some literature/papers talking about this?

I found some questions along the way like this and this but they seem not to provide an answer to my question.

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  • $\begingroup$ A slight remark is that there all multiple methods for renormalization and as far as i know not all of them have been shown to be equivalent. $\endgroup$
    – NDewolf
    Aug 30, 2020 at 12:32
  • $\begingroup$ I intended the question to refer to the renormalization of the standard model. I edited the question to reflect it. $\endgroup$
    – Sjoerd222888
    Aug 30, 2020 at 19:28
  • $\begingroup$ The idea of renormalisation itself seems pretty well-defined to me, once you say that you define the theory with a regulator, say a cutoff $\Lambda$, and then add counterterms such that the dependence on the regulator drops. Then the limit $\Lambda \rightarrow \infty$ is perfectly safe. Maybe the problems you refer to concern more like renormalisability to all orders, which I think are also related to other mathematical problems that QFT has (which are plenty). I am only midly familiar with such all order arguments but the ones that I have seen seem far from mathematical rigour. $\endgroup$
    – jkb1603
    Sep 1, 2020 at 16:59

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