The Dirac equation can be derived basically "directly" from the Representation theory of the Lorentz group for the spin half representation, this is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) 6.3 "Dirac Equation".

The Diract equation is the spacetime symmetry part of the quantum electrodynamics Lagrangian, i.e. is describes how spin half particles behave without interactions. The full quantum electrodynamics Lagrangian can then be reached by adding the $U(1)$ internal symmetry.

As mentioned at spin comes naturally when adding relativity to quantum mechanics, this same method allows us to analogously derive the equations for other spin numbers.

Bibliography:

This idealization does not seems to be possible at all in the context of Maxwell's equations with pointlike particles.

Managed to upload the content from the static website cirosantilli.com (OurBigBook Markup source at github.com/cirosantilli/cirosantilli.github.io) to ourbigbook.com/cirosantilli.

Although most of the key requirements were already in place since the last update, as usual doing things with the complex reference content stresses the system further and leads to the exposition of several new bugs.

The upload of OurBigBook Markup files to ourbigbook.com was done with the newly added OurBigBook CLI ourbigbook --web option. Although fully exposed to end users, the setup is not super efficient: a trully decent implementation should only upload changed files, and would basically mean reimplementing/using Git, since version diffing is what Git shines at. But I've decided not to put much emphasis on CLI upload for now, since it is expected that initially the majority of users will use the Web UI only. The functionality was added primarily to upload the reference content.

This is a major milestone, as the new content can start attracting new users, and makes the purpose of the website much clearer. Just having this more realistic content also immediately highlighted what the next development steps need to be.

Once v1.0 is reached, I will actually make all internal links of cirosantilli.com to point to ourbigbook.com/cirosantilli to try and drive some more traffic.

The new content blows up by far the limit of the free Heroku PostgreSQL database of 10k lines. This meant that I needed to upgrade the Heroku Postgres plugin from the free Hobby Dev to the 9 USD/month Hobby Basic: elements.heroku.com/addons/heroku-postgresql, so now hosting costs will increase from 7 USD/month for the dyno to 7 + 9 = 16 UDS/month. After this upgrade and uploading all of cirosantilli.com to ourbigbook.com, Heroku dashboard reads reads:so clearly if we are ever forced to upgrade plans again, it means that a bunch of people are using the website and that things are going very very well! Happy how this storage cost turned out so far.

One key limitation found was that Heroku RAM memory is quite limited at 512MB, and JavaScript is not exactly the most memory economical language out there. Started investigation at: github.com/ourbigbook/ourbigbook/issues/230 Initially working around that by simply splitting the largest files. We were just on the verge of what could be ran however luckily, so a few dozen splits was enough, it managed to handle 70 kB OurBigBook Markup inputs. So hopefully if we manage to optimize a bit more we will be able to set a maximum size of 100 kB and still have a good safety margin.

You can now write:in lieu of the old:

Every article now has a (very basic) GitHub-like issue tracker. Comments now go under issues, and issues go under articles. Issues themselves are very similar to articles, with a title and a body.

This was part of 1.0, but not the first priority, but I did it now anyways because I'm trying to do all the database changes ASAP as I'm not in the mood to write database migrations.

Here's an example:

The simplest harmonic oscillator system.

Example: sqlite/ip.c, adapted from www.sqlite.org/loadext.html, also mentioned explained at: stackoverflow.com/questions/7638238/sqlite-ip-address-storage/76520885#76520885.

Sample usage in the test program: sqlite/test.sh.

Docs: www.sqlite.org/loadext.html

Each transaction isolation level specifies what can or cannot happen when two queries are being run in parallel, i.e.: the memory semantics of the system.

Remember that queries can affects thousands of rows, and database systems like PostgreSQL can run multiple such queries at the same time.

Good summary on the PostgreSQL page: www.postgresql.org/docs/14/transaction-iso.html

Implementation specifics:

A squeezed coherent state of light.

Waste of time sub-sites that should instead be merged into Stack Overflow as different tags.

Nowhere is this waste more visible than at: cs50.stackexchange.com/. A website just for some specific course that is completely covered by other sites of the network? What a humongous waste!!!

Paywalled at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.7.43

The first published experimental observation of the magnetic flux quantum.

The paper that follows it in the journal is also of interest, "Theoretical Considerations Concerning Quantized Magnetic Flux In Superconducting Cylinders" by N. Byers and C. N. Yang, it starts:So there was some previous confusion about the flux quantum due to the presence of Cooper pairs or not.

Dumping the fitures at: archive.org/details/experimental-evidence-for-quantized-flux-in-superconducting-cylinders One day we can also dump the paper scans when it goes into the public domain in 2056! Public domain scientific paper by year.

One may dream.

If they belive that their reputation is a representative meaningful metric, then it should be fine!

And if not, then they should fix it.

Notably, more people would try to "game" the system by quickly answering lots of small impact answers which could tilt things off a bit. Not to mention straight out fraud.

So basically less money into developers doing useless new features for the website, and more money back into meaningful contributors.

How about 2k USD / month for the number one contributor of the year, going linearly down to 0 for the 200th? This would be 100k USD / month, so about 12 developers.

As of 2019, the more formal name for particle physics, which is notably missing general relativity to achieve the theory of everything.

cds.cern.ch/record/799984/files/0401010.pdf The Making of the Standard Model by Steven Weinberg mentions three crucial elements that made up the standard model post earlier less generalized quantum electrodynamics understandings