Renormalization: The Art of Erasing Infinity

Renormalization is perhaps one of the most controversial topics in high-energy physics. On the surface, it seems entirely ad-hoc and made up to subtract divergences which appear in particle physics calculations. However, when we dig a little deeper, we see that renormalization is nothing to be afraid of and that it is perfectly mathematically valid!

0:00 Intro
1:20 Source of Divergences
3:30 A Simple Analogy
8:20 Renormalization in Particle Physics

[Williamtolduso]

Every qft lecturer should just link to this video instead of trying to explain it in front of a live audience.
Great job

[jeffreyhersh]

Brings me back to when I was working on my doctoral thesis in the late 90s. Applied a technique called operator regularization along with renormalization to generate effective field terms of the Higgs sector from supersymmetric models. Those calculations were a bear and I remember factors of i and 2 being the bane of my existence doing them.

[praveenb]

Reminds me of the story that imaginary numbers were first invented as a part of an intermediate step when solving cubic equations with real roots. They cancelled out and didn't appear in the solution but were an indispensable part of the calculation process.

[sadface]

Renormalization is one of those underrate developement in physics. When we talk about the success of the standard model it should be in reference to its taming via renormalization.

[luckyluckydog]

the best explanation of renormalization on youtube! Thanks

[piercingspear]

After going around blindly in the past 2 weeks of my QFT lecture about renormalization, I finally have an idea on why they do that and why is it legal lol. Thank you so much about the video! xD

[alberto_]

I am working in top quark pole mass measurements and your explanation was great. It remind me to my old QCD lessons :)

[petit.croissant]

im really grateful for this video; you manage to explain such a perplexing topic in physics in a simple and concise manner!!

[christiannguyen]

Woah, feels like im re-reading schwartz ..great overview!, this is awesome to put these high level videos out there

[paulkohl]

20:16 But it is shuffling ∞'s under the rug! And it is all because a non-normalizable basis for the particle wave-functions was chosen when QED was developed (free plane-wave sol. to Dirac eq.), and that is just some of the mathematical problems with QFT: Haag's Thm; Equal Time instead of Equal Event Comm. Rel.; Dyson's Normal Ordering v. Time Ordering Hack, "effective" field theory which allows one to effectively massage whatever answer one wants into a Lagrangian; Canonical Quantization treating clockmaker time in a Newtonian, not SR invariant, way; etc. etc.

[doodelay]

In this video the creator is fully convinced this isn't a problem but so many other theoretical physicists like Feynman, Freeman Dyson, Dirac and many others believe it a massive issue.

So it isn't that we don't understand the counterbalancing act, it's that even having to counter balance in this way is itself suspect as there's no natural counterbalance to speak of. It's pure math.

[DavidRodriguez-dyer]

11:04 "If we define these counterfactors so that it exactly cancels these divergences" I don't see a logical or physical justification for doing that.

[ПавелБережной-цг]

I never understood this topic in my classes, I just repeated calculations after lecturer, but I definetely understand something now. Thank you very much

[nikhilhatwar]

For someone who is trying to study QFT on his own, this video is gold. Thank you so much! Looking forward to seeing other videos by you.

[kerbydimayuga]

LOVE YOUR EXPLANATION! Do you recommend any books on perturbation theories and renormalisation? I'd love to deepen my knowledge of this. I just know the bare minimum when I passed my QFT exam

[paulkohl]

Caveat emptor, there are many renormalization schemes. Each scheme has its own advantages and problems, but all of them get way more complicated the more loops one has to consider.

[sambhavgupta]

Amazing explanation!! you are one of the few best explainers out there for physics. Keep working on these.

[frotzecht]

This is a beautiful exposé. I would just like to add that there is also a physical reason why renormalization is needed, independent of divergences. Namely, in a perturbation theory there’s a mismatch between the measured inputs which always include all orders of the perturbation series and the values used in the calculations which obviously don’t. Especially when taking a value measured in process A and using it to calculate process B it is by no means clear that the perturbation series will work in such a way that this works. The RG equations are a formalization of the requirement that this works. One can construct classical theories where one has this mismatch, e.g. taking Newtonian gravity and adding a perturbation to the potential, what is the mass that enters the calculations? The new gravitational mass or the inertial mass? In the Einstein case both will have to be the same, but then the perturbation series has to work in such a way that maintain this equality up to the order of perturbation considered.

[DMBall]

"Renormalization" should come into wider use. For instance Samuel Bankman-Fried really didn't steal all those billions; he renormalized them.

[lalalalaphysics]

Let me get this straight. By introducing adjustable parameters to make the equations work by plugging in somewhat random functions to eliminate any infinities?