Theory that describes electrons and photons really well, and as Feynman puts it "accounts very precisely for all physical phenomena we have ever observed, except for gravity and nuclear physics" ("including the laughter of the crowd" ;-)).

Learning it is one of Ciro Santilli's main intellectual fetishes.

While Ciro acknowledges that QED is intrinsically challenging due to the wide range or requirements (quantum mechanics, special relativity and electromagnetism), Ciro feels that there is a glaring gap in this moneyless market for a learning material that follows the Middle Way as mentioned at: the missing link between basic and advanced. Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) is one of the best attempts so far, but it falls a bit too close to the superficial side of things, if only Feynman hadn't assumed that the audience doesn't know any mathematics...

The funny thing is that when Ciro Santilli's mother retired, learning it (or as she put it: "how photons and electrons interact") was also one of her retirement plans. She is a pharmacist by training, and doesn't know much mathematics, and her English was somewhat limited. Oh, she also wanted to learn how photosynthesis works (possibly not fully understood by science as that time, 2020). Ambitious old lady!!!

Experiments: quantum electrodynamics experiments.

Combines special relativity with more classical quantum mechanics, but further generalizing the Dirac equation, which also does that: Dirac equation vs quantum electrodynamics. The name "relativistic" likely doesn't need to appear on the title of QED because Maxwell's equations require special relativity, so just having "electro-" in the title is enough.

Before QED, the most advanced theory was that of the Dirac equation, which was already relativistic but TODO what was missing there exactly?

As summarized at: youtube.com/watch?v=_AZdvtf6hPU?t=305 Quantum Field Theory lecture at the African Summer Theory Institute 1 of 4 by Anthony Zee (2004):

- classical mechanics describes large and slow objects
- special relativity describes large and fast objects (they are getting close to the speed of light, so we have to consider relativity)
- classical quantum mechanics describes small and slow objects.
- QED describes objects that are both small and fast

That video also mentions the interesting idea that:Therefore, for small timescales, energy can vary a lot. But mass is equivalent to energy. Therefore, for small time scale, particles can appear and disappear wildly.

- in special relativity, we have the mass-energy equivalence
- in quantum mechanics, thinking along the time-energy uncertainty principle, $ΔE∼Δt1 $

QED is the first quantum field theory fully developed. That framework was later extended to also include the weak interaction and strong interaction. As a result, it is perhaps easier to just Google for "Quantum Field Theory" if you want to learn QED, since QFT is more general and has more resources available generally.

Like in more general quantum field theory, there is on field for each particle type. In quantum field theory, there are only two fields to worry about:

- photon field
- electromagnetism field

Experiments explained by QED but not by the Dirac equation:

- Lamb shift: by far the most famous one
- hyperfine structure TODO confirm
- anomalous magnetic dipole moment of the electron

2s/2p energy split in the hydrogen emission spectrum, not predicted by the Dirac equation, but explained by quantum electrodynamics, which is one of the first great triumphs of that theory.

Note that for atoms with multiple electrons, 2s/2p shifts are expected: Why does 2s have less energy than 1s if they have the same principal quantum number?. The surprise was observing that on hydrogen which only has one electron.

Initial experiment: Lamb-Retherford experiment.

On the return from the train from the Shelter Island Conference in New York, Hans Bethe managed to do a non-relativistic calculation of the Lamb shift. He then published as The Electromagnetic Shift of Energy Levels by Hans Bethe (1947) which is still paywalled as of 2021, fuck me: journals.aps.org/pr/abstract/10.1103/PhysRev.72.339 by Physical Review.

The Electromagnetic Shift of Energy Levels Freeman Dyson (1948) published on Physical Review is apparently a relativistic analysis of the same: journals.aps.org/pr/abstract/10.1103/PhysRev.73.617 also paywalled as of 2021.

TODO how do the infinities show up, and how did people solve them?

www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)

Published as "Fine Structure of the Hydrogen Atom by a Microwave Method" by Willis Lamb and Robert Retherford (1947) on Physical Review. This one actually has open accesses as of 2021, miracle! journals.aps.org/pr/pdf/10.1103/PhysRev.72.241

Microwave technology was developed in World War II for radar, notably at the MIT Radiation Laboratory. Before that, people were using much higher frequencies such as the visible spectrum. But to detect small energy differences, you need to look into longer wavelengths.

This experiment was fundamental to the development of quantum electrodynamics. As mentioned at Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "Shrinking the infinities", before the experiment, people already knew that trying to add electromagnetism to the Dirac equation led to infinities using previous methods, and something needed to change urgently. However for the first time now the theorists had one precise number to try and hack their formulas to reach, not just a philosophical debate about infinities, and this led to major breakthroughs. The same book also describes the experiment briefly as:

Willis Lamb had just shined a beam of microwaves onto a hot wisp of hydrogen blowing from an oven.

It is two pages and a half long.

They were at Columbia University in the Columbia Radiation Laboratory. Robert was Willis' graduate student.

Previous less experiments had already hinted at this effect, but they were too imprecise to be sure.

Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) mentions it several times.

This was one of the first two great successes of quantum electrodynamics, the other one being the Lamb shift.

In youtu.be/UKbp85zpdcY?t=52 from freeman Dyson Web of Stories interview (1998) Dyson mentions that the original key experiment was from Kusch and Foley from Columbia University, and that in 1948, Julian Schwinger reached the correct value from his calculations.

Apparently first published at The Magnetic Moment of the Electron by Kusch and Foley (1948).

Bibliography:

- www.youtube.com/watch?v=Ix-3LQhElvU Anomalous Magnetic Moment Of The Electron | One Loop Quantum Correction | Quantum Electrodynamics by Dietterich Labs (2019)

Published on Physical Review by Polykarp Kusch and Foley.

journals.aps.org/pr/abstract/10.1103/PhysRev.74.250, paywall as of 2021.

TODO: in high level terms, why is QED more general than just solving the Dirac equation, and therefore explaining quantum electrodynamics experiments?

Also, is it just a bunch of differential equation (like the Dirac equation itself), or does it have some other more complicated mathematical formulation, as seems to be the case? Why do we need something more complicated than

Advanced quantum mechanics by Freeman Dyson (1951) mentions:

A Relativistic Quantum Theory of a Finite Number of Particles is Impossible.

Bibliography:

- physics.stackexchange.com/questions/101307/dirac-equation-in-qft-vs-relativistic-qm
- physics.stackexchange.com/questions/44188/what-is-the-relativistic-particle-in-a-box/44309#44309 says:
By several reasons explained in textbooks, the Dirac equation is not a valid wavefunction equation. You can solve it and find solutions, but those solutions cannot be interpreted as wavefunctions for a particle

- physics.stackexchange.com/questions/64206/why-is-the-dirac-equation-not-used-for-calculations
- www.physicsforums.com/threads/is-diracs-equation-still-useful-after-qed-is-developed.663994/

$L_{QED}=ψˉ (iℏcD/−mc_{2})ψ−4μ_{0}1 F_{μν}F_{μν}$

- $F$ is the electromagnetic tensor

Note that this is the sum of the:Note that the relationship between $ψ$ and $F$ is not explicit. However, if we knew what type of particle we were talking about, e.g. electron, then the knowledge of psi would also give the charge distribution and therefore $F$

- Dirac Lagrangian, which only describes the "inertia of bodies" part of the equation
- the electromagnetic interaction term $4μ_{0}1 F_{μν}F_{μν}$, which describes term describes forces

As mentioned at the beginning of Quantum Field Theory lecture notes by David Tong (2007):

- by "Lagrangian" we mean Lagrangian density
- the generalized coordinates of the Lagrangian are fields

Like the rest of the Standard Model Lagrangian, this can be split into two parts:

- spacetime symmetry: reaches the derivation of the Dirac equation, but has no interactions
- add the $U(1)$ internal symmetry to add interactions, which reaches the full equation

TODO find/create decent answer.

I think the best answer is something along:

- local symmetries of the Lagrangian imply conserved currents. $U(1)$ gives conserved charges.
- OK now. We want a local $U(1)$ symmetry. And we also want:Given all of that, the most obvious and direct thing we reach a guess at the quantum electrodynamics Lagrangian is Video "Deriving the qED Lagrangian by Dietterich Labs (2018)"
- Dirac equation: quantum relativistic Newton's laws that specify what forces do to the fields
- electromagnetism: specifies what causes forces based on currents. But not what it does to masses.

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.

From Video "Lorenzo Sadun on the "Yang-Mills and Mass Gap" Millennium problem":

- www.youtube.com/watch?v=pCQ9GIqpGBI&t=1663s mentions this idea first came about from Hermann Weyl.
- youtu.be/pCQ9GIqpGBI?t=2827 mentions that in that case the curvature is given by the electromagnetic tensor.

Bibliography:

- www.youtube.com/watch?v=qtf6U3FfDNQ Symmetry and Quantum Electrodynamics (The Standard Model Part 1) by ZAP Physics (2021)
- www.youtube.com/watch?v=OQF7kkWjVWM The Symmetry and Simplicity of the Laws of Nature and the Higgs Boson by Juan Maldacena (2012). Meh, also too basic.

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.

- www.youtube.com/watch?v=fG52mXN-uWI The Secrets of Feynman Diagrams | Space Time by PBS Space Time (2017)

No, but why?

What they presented on richard Feynman's first seminar in 1941. Does not include quantum mechanics it seems.

TODO understand this stuff:

fafnir.phyast.pitt.edu/py3765/ Phys3765 Advanced Quantum Mechanics -- QFT-I Fall 2012 by E.S. Swanson mentions several milestone texts including:

Lecture notes that were apparently very popular at Cornell University. In this period he was actively synthesizing the revolutionary bullshit Richard Feynman and Julian Schwinger were writing and making it understandable to the more general physicist audience, so it might be a good reading.

We shall not develop straightaway a correct theory including many particles. Instead we follow the historical development. We try to make a relativistic quantum theory of one particle, find out how far we can go and where we get into trouble.

Recommended by Ron Maimon at physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics/18643#18643.

Julian Schwinger's selection of academic papers by himself and others.

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

- 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:where$E=f(1,2,m)P=f(1,2,0)$
`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:summed over all possible $D$ Spacetime points.$c×E(A,D)×E(D,B)×P(B,C)$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.

Sample playlist: www.youtube.com/playlist?list=PLW_HsOU6YZRkdhFFznHNEfua9NK3deBQy

Basically the same content as: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), but maybe there is some merit to this talk, as it is a bit more direct in some points. This is consistent with what is mentioned at www.feynman.com/science/qed-lectures-in-new-zealand/ that the Auckland lecture was the first attempt.

Some more information at: iucat.iu.edu/iub/5327621

By Mill Valley, CA based producer "Sound Photosynthesis", some info on their website: sound.photosynthesis.com/Richard_Feynman.html

They are mostly a New Age production company it seems, which highlights Feynman's absolute cult status. E.g. on the last video, he's not wearing shoes, like a proper guru.

Feynman liked to meet all kinds of weird people, and at some point he got interested in the New Age Esalen Institute. Surely You're Joking, Mr. Feynman this kind of experience a bit, there was nude bathing on a pool that oversaw the sea, and a guy offered to give a massage to the he nude girl and the accepted.

youtu.be/rZvgGekvHest=5105 actually talks about spin, notably that the endpoint events also have a spin, and that the transition rules take spin into account by rotating thing, and that the transition rules take spin into account by rotating things.

Available for free online rent on the Internet Archive: archive.org/details/qedmenwhomadeitd0000schw

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.

From University of Alberta.