Like the rest of the Standard Model Lagrangian, this can be split into two parts:
Video 1.
Deriving the qED Lagrangian by Dietterich Labs (2018)
Source.
As mentioned at the start of the video, he starts with the Dirac equation Lagrangian derived in a previous video. It has nothing to do with electromagnetism specifically.
He notes that that Dirac Lagrangian, besides being globally Lorentz invariant, it also also has a global invariance.
However, it does not have a local invariance if the transformation depends on the point in spacetime.
He doesn't mention it, but I think this is highly desirable, because in general local symmetries of the Lagrangian imply conserved currents, and in this case we want conservation of charges.
To fix that, he adds an extra gauge field (a field of matrices) to the regular derivative, and the resulting derivative has a fancy name: the covariant derivative.
Then finally he notes that this gauge field he had to add has to transform exactly like the electromagnetic four-potential!
So he uses that as the gauge, and also adds in the Maxwell Lagrangian in the same go. It is kind of a guess, but it is a natural guess, and it turns out to be correct.
TODO find/create decent answer.
I think the best answer is something along:
A basic non-precise intuition is that a good model of reality is that electrons do not "interact with one another directly via the electromagnetic field".
A better model happens to be the quantum field theory view that the electromagnetic field interacts with the photon field but not directly with itself, and then the photon field interacts with parts of the electromagnetic field further away.
The more precise statement is that the photon field is a gauge field of the electromagnetic force under local U(1) symmetry, which is described by a Lie group. TODO understand.
This idea was first applied in general relativity, where Einstein understood that the "force of gravity" can be understood just in terms of symmetry and curvature of space. This was later applied o quantum electrodynamics and the entire Standard Model.
Bibliography:
Feynman diagram by Ciro Santilli 37 Updated 2025-07-16
I think they are a tool to calculate the probability of different types of particle decays and particle collision outcomes. TODO Minimal example of that.
And they can be derived from a more complete quantum electrodynamics formulation via perturbation theory.
At Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), an intuitive explanation of them in termes of sum of products of propagators is given.
Talk title shown on intro: "Today's Answers to Newton's Queries about Light".
6 hour lecture, where he tries to explain it to an audience that does not know any modern physics. This is a noble effort.
Part of The Douglas Robb Memorial Lectures lecture series.
Feynman apparently also made a book adaptation: QED: The Strange Theory of Light and Matter. That book is basically word by word the same as the presentation, including the diagrams.
According to www.feynman.com/science/qed-lectures-in-new-zealand/ the official upload is at www.vega.org.uk/video/subseries/8 and Vega does show up as a watermark on the video (though it is too pixilated to guess without knowing it), a project that has been discontinued and has has a non-permissive license. Newbs.
4 parts:
This talk has the merit of being very experiment oriented on part 2, big kudos: how to teach and learn physics
Video 1.
Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) uploaded by Trev M (2015)
Source. Single upload version. Let's use this one for the timestamps I guess.
This book has formulas on it, which is quite cool!! And the formulas are basically not understandable unless you know the subject pretty well already in advance. It is however possible to skip over them and get back to the little personal stories.
Initially a phenomenological guess to explain the periodic table. Later it was apparently proven properly with the spin-statistics theorem, physics.stackexchange.com/questions/360140/theoretical-proof-of-paulis-exclusion-principle.
And it was understood more and more that basically this is what prevents solids from collapsing into a single nucleus, not electrical repulsion: electron degeneracy pressure!
Bibliography:
Video 1.
The Biggest Ideas in the Universe | 17. Matter by Sean Carroll (2020)
Source.
Video 1.
Electroweak Theory and the Origin of the Fundamental Forces by PBS Space Time (2020)
Source. Unsatisfactory, as usual.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
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    Figure 1.
    Screenshot of the "Derivative" topic page
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    Figure 2.
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    .
    Figure 3.
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    Figure 4.
    Visual Studio Code extension tree navigation
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    Figure 5.
    Web editor
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    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
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