Can someone explain to me the processes of renormalization and regularization used in quantum field theory and similar fields in a way that a pure mathematician might make sense of it? Is there a mathematically rigorous way to go about doing them? Could you give an example of a basic renormalization and explain why it was necessary?
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4See answers [here](http://mathoverflow.net/q/62770). – Start wearing purple Aug 02 '13 at 09:33

That page seems a little advanced. My background is mathematical logic, so this is all very foreign to me. – greg Aug 02 '13 at 12:39

1In my humble opinion, renormalization is simply removing some specific "wrongness" introduced in QFT equations due to unjustified selfaction anzats. Warning: my opinion is not widely accepted. – Vladimir Kalitvianski Nov 23 '14 at 15:02

Maybe this can be helpful: https://mathoverflow.net/questions/115743/analgebraofintegrals/342651#342651 – Anixx Dec 17 '20 at 16:15
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Maybe you should start reading a bit about the history of QFT as it would give the justification for the mathematics behind renormalization. A good starting point could be:
I  https://plato.stanford.edu/entries/quantumfieldtheory/qfthistory.html
You won't, however, be completely free from physics while trying to grasp the concepts. I found a paper that claims to explain QFT and RG (renormalization group) in just 11 pages.
II  https://arxiv.org/pdf/1311.4897.pdf
Not sure if it is enough, but you might give it a try. There is also the text from Weinberg about QFT development:
III  http://www.fafnir.phyast.pitt.edu/py3765/WeinbergQFThistory.pdf
That may help on organizing the subjects in your head.
Lincon Ribeiro
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