Ciro Santilli @cirosantilli 35

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

U (1)

invariance.

However, it does not have a local invariance if the

U (1)

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_{μ}

(a field of

4 \times 4

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.

www.youtube.com/watch?v=IFRyN3fQMO8&lc=UgzNGkLXdwcSl7z8Lap4AaABAg

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Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) by

Ciro Santilli 35  Updated 2025-01-10  +Created 1970-01-01

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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:

Part 1: is saying "photons exist"
Part 2: is amazing, and describes how photons move as a sum of all possible paths, not sure if it is relativistic at all though, and suggests that something is minimized in that calculation (the action)
Part 3: is where he hopelessly tries to explain the crucial part of how electrons join the picture in a similar manner to how photons do.
He does make the link to light, saying that there is a function $P (A, B)$ which gives the amplitude for a photon going from A to B, where A and B are spacetime events.
And then he mentions that there is a similar function $E (A, B)$ for an electron to go from A to B, but says that that function is too complicated, and gives no intuition unlike the photon one.
He does not mention it, but P and E are the so called propagators.
This is likely the path integral formulation of QED.
On Quantum Mechanical View of Reality by Richard Feynman (1983) he mentions that $E$ is a Bessel function, without giving further detail.
And also mentions that:
$E = f (1, 2, m) P = f (1, 2, 0)$
(1)
where m is basically a scale factor.
such that both are very similar. And that something similar holds for many other particles.
And then, when you draw a Feynman diagram, e.g. electron emits photon and both are detected at given positions, you sum over all the possibilities, each amplitude is given by:
$c \times E (A, D) \times E (D, B) \times P (B, C)$
(2)
summed over all possible $D$ Spacetime points.
This is basically well said at: youtu.be/rZvgGekvHes?t=3349 from Quantum Mechanical View of Reality by Richard Feynman (1983).
TODO: how do electron velocities affect where they are likely to end up? $E (A, D)$ suggests the probability only depends on the spacetime points.
Also, this clarifies why computations in QED are so insane: you have to sum over every possible point in space!!! TODO but then how do we calculate anything at all in practice?
Part 4: known problems with QED and thoughts on QCD. Boring.