Particle Physics is Founded on This Principle!

Conservation laws, symmetries, and in particular gauge symmetries are fundamental to the construction of the standard model of particle physics. And as we've seen in past videos, the link that connects symmetries and conservation laws is Noether's theorem. In this video, we'll see how it all extends to field theories. We'll learn to formulate a local conservation law by writing down its continuity equation, which describes how charge is conserved in any region of space. Then we'll see how these conservation laws appear any time we have a field theory with a continuous symmetry. We'll learn about the symmetry of electromagnetism, called U(1), that leads to the conservation of electric charge. And finally, we'll see how to write down the simplest example of a gauge theory by coupling to the electromagnetic potential. The global U(1) symmetry becomes a local symmetry thanks to the covariant derivative, and we arrive at a U(1) gauge theory! The standard model is a generalization of all this.

About physics mini lessons:
In these intermediate-level physics lessons, I'll try to give you a self-contained introduction to some fascinating physics topics. If you're just getting started on your physics journey, you might not understand every single detail in every video---that's totally fine! What I'm really hoping is that you'll be inspired to go off and keep learning more on your own.

About me:

[devamjani]

None of this would have been possible without the Noether's theorem. It is really the foundation of entire mathematical physics. She deserves much more recognition.

[Kram]

omg a channel that actually is happy to do like mid-level-ish physics, rather than either total beginner stuff that assumes this is too scary or advanced cutting-edge research lectures that assume you already know this stuff by heart
Really glad to see this!

[b_stone_]

I'm doing my PhD in theoretical high-energy physics, and I have to say this is one of the best intuitive introductions to gauge theory I've ever seen. I've been binging your videos, keep it up!

[eirninlovesyou]

I truly love this channel! Every physics channel on YouTube is either extremely oversimplified analogies creating more questions than they answer, or actual PhD level lecture notes and there's rarely any channel which actually explores why the mathematics are they way they are! Thanks for the work :)

[yairraz]

Absolute gold, please do a video on the Higgs mechanism

[DeathEnducer]

I'm an Accelerator physicist and everything I've derived started from maxwell equations. I'm obsessed with going deeper to derive Maxwell equations themselves, this is exactly what i needed 💯

[virtualknight]

I just spent 2 months to understand this subjects separately from different sources and end up in deep confusion now you saved my day thank you so much

[exciton]

This channel explains very complicated topics in a very simple way, but does not oversimplified it. Thanks for sharing your knowledge. Marvelous!!!

[kka]

You bring so much insight and clarity to some of the most advanced concepts in physics to make it so accessible to us, engineers. Always looking forward to your videos.

[sirwinston]

BSChE here, about ready to retire in about a year and go back to my alma mater to get a BS-Physics. I have been watching a lot of videos (incl. MIT OpenCourseWare) and reading various books (Linus Pauling 1935, Griffiths ED and QM, and my old Halliday/Resnick beginners book). I have to say this was way over my head but... one of these days I am going to understand all of this... I hope! Thank you Elliot! Great videos.

[jayaceto]

@3:45 - Yes, please do a video on the Higgs mechanism and other aspects of the standard model. Maybe some videos on the different types of QFT’s that there are, things like QED, QCD and lattice QCD, the weak interaction theory, the electroweak theory etc. Also topics like the eight-fold way method, S matrices, the spin-statistics theorem, Feynman’s path integral and Feynman diagrams for different types of scattering interactions, scattering cross sections and decay-widths, abelian and non-abelian gauge theories, neutrino flavor oscillations and the ways neutrino masses are incorporated into the standard model, and other topics of the standard model of your choice that you think are interesting. Just some ideas if you feel so compelled please. Thanks 😁. Also, the videos you have done so far are great and I have learned much from them 👍👍. I am very appreciative as I know videos like these take a lot of careful thought and time, and are not easy to do. Keep up the good work!

[lardmaster]

This video finally answers a question that’s been bothering me for a long time… why is charge conserved? To summarise,

1) Conserving charge means satisfying a charge continuity equation.
2) Lagrangian density of a field is rotationally symmetric in complex space as it is the product of a complex field and its conjugate, which depends only on the magnitude of the field and not its angle.
3) From Noether’s Theorem, if we choose a symmetry such that dL = 0 - such as the rotation symmetry in complex space - then we get a conserved quantity Q. This quantity is a bunch of derivatives in space and time now since the field is itself also a function of space and time. This is the continuity equation which conserves charge.

I’m not clear on why taking the covariant derivative preserves symmetry - in changing the definition of the derivative, why should the system be symmetric in the same way as with normal derivatives?

On another note, I would really look forward to more in-depth explanations on the last bit involving Maxwell’s Equations, and perhaps a video or problem sheet on how substituting plane waves into N gives rise to the number of particles minus the number of anti-particles.

[MusaHusseini]

Great content and superb explanation of the concepts pertaining to field theory. Coming from an Electrical Engineering background with basic foundation in undergrad Physics and Mathematics, I can confidently say this is the first time I come across a very high quality video that deals with particle Physics in a very elegant and logical manner. Thank you so much for working so hard on producing this video, cannot wait to start learning about String Theory from your channel (it would be a great tribute to the late Joseph Polchinski).

[Deniz-lexp]

Please keep this series going, I can't wait for more videos on this topic. Really well done.

[monissiddiqui]

When I was studying electromagnetics in the third year of an engineering program, our professor mentioned gauge theory as an aside and I was very intrigued. This led me to a furious night of wikipedia binging, link chasing and textbook hoarding but I was still left hopelessly confused. I was disappointed that despite having studied so much mathematics I was still so far away from understanding these ideas. A semester later after being fed up with the lack of math and physics, I transferred over to the math department and graduated with a double major in math 😅

Now years after my undergrad I'm self-studying physics and am this close
👉👈 to finally understanding gauge theory. Your channel helps a bunch, I swear.

It's a fascinating time to be alive, but my past self is super jealous of my present self for having this video! Thanks for all these wonderful videos 🙂

[bulldozer]

This video is incredible. Your explanations are fantastic. I still don't *get* every part, but you've given me a great foundation to work from. Thank you!

[jamesbentonticer]

I just finished Noether's Theorem, ready for more symmetry! Bring on the Higgs!

[zacmilne]

This was great! I have a background in math and physics and I felt that the derivations here were pleasantly explained. Thanks for making videos like this! So many videos on the subject skip the details but I love them and you do a great job explaining them.

[ivanbrekotkin]

It is ironic that this channel appeared in my life along with Bogolyubov's book "Introduction to Quantum Field Theory". Thank you for your work, you help to better understand the material!

[jaw]

Thank you so much for what you're doing! I'm taking QFT right now and have forgotten some of this from previous grad classes and have struggled all semester (especially given the notation)