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.
Adds special relativity to the Schrödinger equation, and the following conclusions come basically as a direct consequence of this!
Experiments explained:
- spontaneous emission coefficients.
- fine structure, notably for example Dirac equation solution for the hydrogen atom
- antimatter
- particle creation and annihilation
Experiments not explained: those that quantum electrodynamics explains like:See also: Dirac equation vs quantum electrodynamics.
- Lamb shift
- TODO: quantization of the electromagnetic field as photons?
The Dirac equation is a set of 4 partial differential equations on 4 complex valued wave functions. The full explicit form in Planck units is shown e.g. in Video 1. "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=1010:Then as done at physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600 from why are complex numbers used in the Schrodinger equation?, we could further split those equations up into a system of 8 equations on 8 real-valued functions.
Equation 1.
Expanded Dirac equation in Planck units
. Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)
Source. PHYS 485 Lecture 14: The Dirac Equation by Roger Moore (2016)
Source. 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,
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
Lecture 01 | Overview of Quantum Field Theory by Markus Luty (2013)
Source. This takes quite a direct approach, one cool thing he says is how we have to be careful with adding special relativity to the Schrödinger equation to avoid faster-than-light information.The first really good quantum mechanics theory made compatible with special relativity was the Dirac equation.
And then came quantum electrodynamics to improve it: Dirac equation vs quantum electrodynamics.
TODO: does it use full blown QED, or just something intermediate?
www.youtube.com/watch?v=NtnsHtYYKf0 "Mercury and Relativity - Periodic Table of Videos" by Periodic Videos (2013). Doesn't give the key juicy details/intuition. Also mentioned on Wikipedia: en.wikipedia.org/wiki/Relativistic_quantum_chemistry#Mercury
Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)
Source. - youtu.be/tR6UebCvFqE?t=23 particle at rest
- youtu.be/tR6UebCvFqE?t=322 unidirectional movement without a potential
- youtu.be/tR6UebCvFqE?t=507 shows that observers in different frames of reference also see different spin. We are reminded of how magnetism is just a side effect of special-relativity.
- youtu.be/tR6UebCvFqE?t=549 Dirac equation solution for the hydrogen atom, final result only + mentions fine structure prediction.