Informal QFT 1 - Classical Gauge Field Theory

Sort of hacked together video. Sorry for the sort of rambling, I didn't have a script.
For whatever reason the final minutes didn't audio record, so sorry for that too.

Some useful stuff:

Teaching electromagnetic field theory using differential forms

The Hamilton-Jacobi Equation : an intuitive approach

The boundary of a boundary principle in field theories and the issue of austerity of the laws of physics

[lucasbrusa-oconnell]

This is an incredible creation! The visuals are extremely well made and the color palette is beautiful as well. Thank you for your time and effort

[MrMentholSlim]

as a failed mathematician and science enthusiast, i appreciate anybody who puts together these kind of things.

[lucacrahaybloklander]

I loved everything about this video! Thank you. Hope you continue the series!

[SirTravelMuffin]

Wonderful! Helped put a lot of pieces together, especially the discussion of level curves of actions as wavefronts in the Hamiltonian!

[plranisch]

I hope I will see more works from you because this series is very beautiful and a great help in understanding QFT!

[averagehummus]

your visual representations are so elegant

[logo]

This was a better explanation than a bunch of popular YouTube videos. You have talent as a teacher. Sad the last part on spin got muted

[edd.]

Regardless of the audio, it’s a great video. 🙏 thank you 🙏

[rezadaneshi]

I recently wanted to learn about Hamiltonian and Lagrangian and this was an excellent simplification of a visualization for both. Till now, the best visualization I had to explain what is energy was whipped chocolate milk compare to just, chocolate milk. This is better.

[raghavsuryan]

Thank you, This was such a good video, and you also are e very good teacher!

[DJsTeLF]

Keep working bro, doing welp so far 😊❤

[soldadodaresistenciaquerre]

Grato Pela Aula excelente conteúdo e ilustrações!!🔥🔥🔥🔥🔥

[Chevelin_X]

This was very good! I like the starting emphasis on principles and then linkage to differential forms!

Did the last few slides not record audio?

[gloop]

Nice video, a small inaccuracy: It's true that the functional derivative of the action is always zero for a physical trajectory, but the action is always a minimum or a saddle point, never a maximum (idea of proof is that you can always add fast oscillations to the trajectory in a way that can only increase the integral).

Edit: a bit further in now. Your way of visualizing a 2-form as a 'malleable eggcrate whose flux tubes have orientation' went a bit fast 😅. I have my own way of thinking about forms, but it's not easy (for me) to translate what an explicit reference to the eggrate analogy like 'the sheets end in a charge' means in realtime. This to say, i might be confused but I think you're mixing up the interpretation of the Maxwell laws, i.e. sheets ending in an electrical charge must surely mean Gauss' law, which follows from d (star) F=J, not from dF=0 as you claim in the video.

[DavidGoldgruber]

How do we know/prove in this case that the electromagnetic 4-potential is the unique, metric compatible, torsionless connection a.k.a. Levi-Civita? In general relativity, we start from the metric compatibility assumption, then we choose Christoffel symbols that are invariant for the exchange of their two lower indices (torsion free). These assumptions select out Levi-Civita for us. But I have never heard of a metric in the U(1) bundle, and I can't imagine one, so I don't even know how to start.
Also, why is the 4-potential a proper 4-vector, when Christoffel symbols don't transform as tensors?
Is it possible to visualise the curvature in the U(1) bundle somehow, like the embedding diagrams of GR? That would be quite helpful, too.

[hyperplastic]

I really liked this video, but some critique: they say people will put up with bad video but not bad audio. It’s really echoey and you even left a burp in there.

[silvercam]

@ARBB Great video! What editing software did you use to make your slides? Very pretty!

[WilliamThompsonH]

What software do you use to make the slides? They are beautiful

[waynelast]

7:06 what optical system has maxima action? Is least time the same as max action?

[MuhammadKhan-gnjp]

Can you please provide me your Discord group details to join? Can you please upload all the lectures covering gauge theory, this is really helpful.