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"handwaving problems away with division by infinity" I'm being very pedantic here but it's a bit better to think of it as subtracting infinity from another inf
by Analog24 10y ago
"handwaving problems away with division by infinity"
I'm being very pedantic here but it's a bit better to think of it as subtracting infinity from another infinity.
- gohrt 10y agoeh, raise the terms as an exponent and subtraction becomes division. :)
- dylukes 10y agoIn log scale yes.
- noobermin 10y agoRenormalization is not the same thing as regularization. Regularization is a mathematical trick while renormalization has a very physical interpretation, for example, its use in statistical mechanics. In QFT, they are related and I think sometimes conflated, which is unfortunate. You can easily describe renormalization without math because it's a physical concept. Regularization is more difficult. If the OP decided divergent integral regularization was an interesting conversation topic then I am on your side.
- aminorex 10y agoPlease do then. Explain it without math, I mean.
- noobermin 10y agoThe entire content of renormalization is summarized as this, given a calculation, you make it match the interaction at some energy. Assuming that the fix is essentially choosing the "scale" of quantities (say, voltage of the electric field, or how strongly electrons tug on other electrons) you are calculating, you fix that scale by making sure that after including it in your theory now, that your result matches the measured interaction at your chosen energy scale exactly. That is renormalization. If you do this, you find that you need to choose a scale that "absorbs" the infinities of your calculations (yes, an "infinite" scale). But, the stuff that is not absorbed is a function of energy, and this actually agrees very well with experiment beyond the scale you normalized to.