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even if I continue reading books about renormalization, I have the same basic doubts.

So we have radiative corrections that give infinites etc.. So what we do is regularize and renormalize the theory.

What is left at the end? Is it true that loops are no longer there since the parameters have eaten them? I mean, the effect of the loops are inside the new parameters?

As a consequence of renormalization, couplings now depend on a scale μ, and physical observables must not depend on it (but perturbation approximation does).

When we say that after renormalization the couplings depend on the energy of the process, is it because they depend on μ? In some formulas I see they depend on q (energy of the process), and on μ (scale), what's the difference?

Last question, often i find mentioned the word "quantum fluctuations". What exactly are these? I mean, it's everywhere written that in the vacuum pair of particles pop up continuously, is there a way to calculate for example how many of them averagely pop up in a certain region of space and interval of time?

Thank you

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# Renormalization and running coupling constant

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