Ciro Santilli @cirosantilli  40

This Heisenberg's breakthrough paper on matrix mechanics which later led to the Schrödinger equation, see also: history of quantum mechanics.

Published on the Zeitschrift für Physik volume 33 page pages 879-893, link.springer.com/article/10.1007%2FBF01328377

Modern overview: www.mat.unimi.it/users/galgani/arch/heisenberg25amer_j_phys.pdf

Basically the same as matrix mechanics it seems, just a bit more generalized.

TODO why do we care about this?

Note that if a group is k-transitive, then it is also k-1-transitive.

A master thesis reviewing its results: scholarworks.sjsu.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=5051&context=etd_theses

The term and idea was first introduced initialized by Hermann Weyl when he was working on combining electromagnetism and general relativity to formulate Maxwell's equations in curved spacetime in 1918 and published as Gravity and electricity by Hermann Weyl (1918). Based on perception that $U(1)$ symmetry implies charge conservation. The same idea was later adapted for quantum electrodynamics, a context in which is has even more impact.

Yup, this one Focks you up.

Second quantization also appears to be useful not only for relativistic quantum mechanics, but also for condensed matter physics. The reason is that the basis idea is to use the number occupation basis. This basis is:

Bibliography:

This one might actually be understandable! It is what Richard Feynman starts to explain at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).

The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.

The path integral formulation can be seen as a generalization of the double-slit experiment to infinitely many slits.

Feynman first stared working it out for non-relativistic quantum mechanics, with the relativistic goal in mind, and only later on he attained the relativistic goal.

TODO why intuitively did he take that approach? Likely is makes it easier to add special relativity.

This approach more directly suggests the idea that quantum particles take all possible paths.

Can you do anything with it? What's the license?