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:
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/
TODO understand in detail.
Advanced quantum mechanics by Freeman Dyson (1951) mentions:
A Relativistic Quantum Theory of a Finite Number of Particles is Impossible.
Atom 2007 Mini Series episode 3:
[The Dirac equation] could only describe a single electron. It fails completely to explain what happens when there is more than one electron present. What was needed was a new theory. A theory which explains how electrons interact with each other.
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