Incoming links: Magnetism
It appears that Maxwell's equations can be derived directly from Coulomb's law + special relativity:
This idea is suggested by the charged particle moving at the same speed of electrons thought experiment, which indicates that magnetism is just a consenquence of special relativity.
TODO. Can't find it easily. Anyone?
This is closely linked to the Pauli exclusion principle.
What does a particle even mean, right? Especially in quantum field theory, where two electrons are just vibrations of a single electron field.
Another issue is that if we consider magnetism, things only make sense if we add special relativity, since Maxwell's equations require special relativity, so a non approximate solution for this will necessarily require full quantum electrodynamics.
As mentioned at lecture 1 youtube.com/watch?video=H3AFzbrqH68&t=555, relativistic quantum mechanical theories like the Dirac equation and Klein-Gordon equation make no sense for a "single particle": they must imply that particles can pop in out of existence.
Bibliography:
- www.youtube.com/watch?v=Og13-bSF9kA&list=PLDfPUNusx1Eo60qx3Od2KLUL4b7VDPo9F "Advanced quantum theory" by Tobias J. Osborne says that the course will essentially cover multi-particle quantum mechanics!
- physics.stackexchange.com/questions/54854/equivalence-between-qft-and-many-particle-qm "Equivalence between QFT and many-particle QM"
- Course: Quantum Many-Body Physics in Condensed Matter by Luis Gregorio Dias (2020) from course: Quantum Many-Body Physics in Condensed Matter by Luis Gregorio Dias (2020) give a good introduction to non-interacting particles