Dirac Lagrangian Updated 2025-07-16
where:
Remember that is a 4-vetor, gamma matrices are 4x4 matrices, so the whole thing comes down to a dot product of two 4-vectors, with a modified by matrix multiplication/derivatives, and the result is a scalar, as expected for a Lagrangian.
Like any other Lagrangian, you can then recover the Dirac equation, which is the corresponding equations of motion, by applying the Euler-Lagrange equation to the Lagrangian.
Discord email notifications Updated 2025-07-16
Discord is useless if you want to participate in more than one large group because of this. It is impossible to get email notification for selected threads you care about.
Divergence in Einstein notation Updated 2025-07-16
First we write a vector field as:
Note how we are denoting each component of as with a raised index.
Then, the divergence can be written in Einstein notation as:
It is common to just omit the variables of the function, so we tend to just say:
or equivalently when referring just to the operator:
Double-slit experiment Updated 2025-07-16
Amazingly confirms the wave particle duality of quantum mechanics.
The effect is even more remarkable when done with individual particles such individual photons or electrons.
Richard Feynman liked to stress how this experiment can illustrate the core ideas of quantum mechanics. Notably, he night have created the infinitely many slits thought experiment which illustrates the path integral formulation.
Nested set model in SQL Updated 2025-07-16
How to implement Nested set model in SQL:
Dulong-Petit law Updated 2025-07-16
Observation that all solids appear to have the same constant heat capacity per mole.
It can be seen as the limit case of an Einstein solid at high temperatures. At lower temperatures, the heat capacity depends on temperature.
Dungeon Crawl Stone Soup Updated 2025-07-16
Appears to be the best classic open source roguelike of the 2020's.
This website is really cool! crawl.akrasiac.org:8080/#lobby You can spectate players live and chat! Also has statistics.
Devs of this game are smart, they have one good in-tree tileset, unlike some other text-based games that didn't have an in-tree option...
Build on Ubuntu 21.10:
sudo apt install build-essential libncursesw5-dev bison flex liblua5.1-0-dev \
libsqlite3-dev libz-dev pkg-config python3-yaml binutils-gold python-is-python3 \
libsdl2-image-dev libsdl2-mixer-dev libsdl2-dev libfreetype6-dev libpng-dev \
fonts-dejavu-core advancecomp pngcrush

git clone --depth 1 --branch 0.28.0 https://github.com/crawl/crawl
cd crawl/crawl-ref/source
echo 0.28-a > util/release_ver
make -j`nproc` TILES=y
./crawl
This launches the UI version already for you.
Eat Just Updated 2025-07-16
Neuralink Updated 2025-07-16
Elon Musk's attempt.

Unlisted articles are being shown, click here to show only listed articles.