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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 internal symmetry to add interactions, which reaches the full equation
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.
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?
Lamb shift by Dr. Nissar Ahmad (2020)
Source. Whiteboard Lecture about the phenomena, includes description of the experiment. Seems quite good.www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)
Mentions that he moved to the USA from the United Kingdom specifically because great experiments were being carried at Columbia University, which is where the Lamb-Retherford experiment was done, and that Isidor Isaac Rabi was the head at the time.
He then explains mass renormalization briefly: instead of calculating from scratch, you just compare the raw electron to the bound electron and take the difference. Both of those have infinities in them, but the difference between them cancels out those infinities.
Hans Bethe - The Lamb shift (1996)
Source. Lamb shift by Vidya-mitra (2018)
Source. 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
The main high level insight seems to be that The Dirac equation does not work for more than one electron.
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:
- 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/
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.
Selected Papers on Quantum Electrodynamics by Julian Schwinger (1958) by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16 Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-166 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 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 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 is a Bessel function, without giving further detail.And also mentions that:where
mis 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 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? 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.
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.- youtu.be/Alj6q4Y0TNE?t=2217: photomultiplier tube
- youtu.be/Alj6q4Y0TNE?t=2410: local hidden-variable theory
- youtu.be/Alj6q4Y0TNE?t=6444: mirror experiment shown at en.wikipedia.org/w/index.php?title=Quantum_electrodynamics&oldid=991301352#Probability_amplitudes
- youtu.be/Alj6q4Y0TNE?t=7309: mirror experiment with a diffraction grating pattern painted black leads to reflection at a weird angle
- youtu.be/Alj6q4Y0TNE?t=7627: detector under water to explain refraction
- youtu.be/Alj6q4Y0TNE?t=8050: explains biconvex spherical lens in terms of minimal times
- youtu.be/Alj6q4Y0TNE?t=8402: mentions that for events in a series, you multiply the complex number of each step
- youtu.be/Alj6q4Y0TNE?t=9270: mentions that the up to this point, ignored:but it should not be too hard to add those
- amplitude shrinks down with distance
- photon polarization
- youtu.be/Alj6q4Y0TNE?t=11697: finally starts electron interaction. First point is to add time of event detection.
- youtu.be/Alj6q4Y0TNE?t=13704: electron between plates, and mentions the word action, without giving a clear enough idea of what it is unfortunately
- youtu.be/Alj6q4Y0TNE?t=14467: mentions positrons going back in time, but does not clarify it well enough
- youtu.be/Alj6q4Y0TNE?t=16614: on the fourth part, half is about frontiers in quantum electrodynamics, and half full blown theory of everything. The QED part goes into renormalization and the large number of parameters of the Standard Model
Quantum electrodynamics by Lifshitz et al. 2nd edition (1982) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16 QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Available for free online rent on the Internet Archive: archive.org/details/qedmenwhomadeitd0000schw
Architecture All Access: Quantum Computing by James Clarke (2021)
Source. python3 -m pip install --user virtualenv
virtualenv .venv
. .venv/bin/activate
pip install -r requirements.txtBased on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!
The private key is made of two randomly generated prime numbers: and . How such large primes are found: how large primes are found for RSA.
The public key is made of:
n = p*q- a randomly chosen integer exponent between
1ande_max = lcm(p -1, q -1), wherelcmis the Least common multiple
Given a plaintext message This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.
m, the encrypted ciphertext version is:c = m^e mod nThe inverse operation of finding the private
m from the public c, e and is however believed to be a hard problem without knowing the factors of n.Bibliography:
- www.comparitech.com/blog/information-security/rsa-encryption/ has a numeric example
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