Ciro Santilli @cirosantilli 37

This is the standard model.

Example: llvm/hello.ll adapted from: llvm.org/docs/LangRef.html#module-structure but without double newline.

To execute it as mentioned at github.com/dfellis/llvm-hello-world we can either use their crazy assembly interpreter, tested on Ubuntu 22.10:This seems to use puts from the C standard library.

Or we can Lower it to assembly of the local machine:which produces:and then we can assemble link and run with gcc:or with clang:hello.s uses the GNU GAS format, which clang is highly compatible with, so both should work in general.

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:

TODO. I think this is the key point. Notably, $U(1)$ symmetry implies charge conservation.

More precisely, each generator of the corresponding Lie algebra leads to one separate conserved current, such that a single symmetry can lead to multiple conserved currents.

This is basically the local symmetry version of Noether's theorem.

Then to maintain charge conservation, we have to maintain local symmetry, which in turn means we have to add a gauge field as shown at Video "Deriving the qED Lagrangian by Dietterich Labs (2018)".

Forces can then be seen as kind of a side effect of this.

Bibliography:

Same motivation as Galilean invariance, but relativistic version of that: we want the laws of physics to have the same form on all inertial frames, so we really want to write them in a way that is Lorentz covariant.

This is just the relativistic version of that which takes the Lorentz transformation into account instead of just the old Galilean transformation.

There are several choices of electromagnetic four-potential that lead to the same physics.

E.g. thinking about the electric potential alone, you could set the zero anywhere, and everything would remain be the same.

The Lorentz gauge is just one such choice. It is however a very popular one, because it is also manifestly Lorentz invariant.

Full set of all possible special relativity symmetries:

In simple and concrete terms. Suppose you observe N particles following different trajectories in Spacetime.

There are two observers traveling at constant speed relative to each other, and so they see different trajectories for those particles:Note that the first two types of transformation are exactly the non-relativistic Galilean transformations.

The Poincare group is the set of all matrices such that such a relationship like this exists between two frames of reference.

A more photon-specific version of the Bloch sphere.

In it, each of the six sides has a clear and simple to understand photon polarization state, either of:

The sphere clearly suggests for example that a rotational or diagonal polarizations are the combination of left/right with the correct phase. This is clearly explained at: Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)".