Ciro Santilli @cirosantilli 37

The rare ones. Notably present in peptidoglycan.

Dan, if you ever Google yourself here, please contact Ciro Santilli: Section "How to contact Ciro Santilli" to do something with OurBigBook.com. Cheers.

Lecture notes: Quantum Field Theory lecture notes by David Tong (2007).

By David Tong.

14 1 hours 20 minute lectures.

The video resolution is extremely low, with images glued as he moves away from what he wrote :-) The beauty of the early Internet.

Two parallel Josephson junctions.

In Ciro's ASCII art circuit diagram notation:

Relates particle momentum and its wavelength, or equivalently, energy and frequency.

The wavelength relation is:but since:the wavelength relation implies:

Particle wavelength can be for example measured very directly on a double-slit experiment.

So if we take for example electrons of different speeds, we should be able to see the diffraction pattern change accordingly.

Notably, convolution can be implemented in terms of GEMM:

A suggested at Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles", it appears that in the Standard Model, the behaviour of each particle can be uniquely defined by the following five numbers:

E.g. for the electron we have:

Once you specify these properties, you could in theory just pluck them into the Standard Model Lagrangian and you could simulate what happens.

Setting new random values for those properties would also allow us to create new particles. It appears unknown why we only see the particles that we do, and why they have the values of properties they have.

Given a matrix $A$ with metric signature containing $m$ positive and $n$ negative entries, the indefinite orthogonal group is the set of all matrices that preserve the associated bilinear form, i.e.:Note that if $A=I$, we just have the standard dot product, and that subcase corresponds to the following definition of the orthogonal group: Section "The orthogonal group is the group of all matrices that preserve the dot product".

As shown at all indefinite orthogonal groups of matrices of equal metric signature are isomorphic, due to the Sylvester's law of inertia, only the metric signature of $A$ matters. E.g., if we take two different matrices with the same metric signature such as:and:both produce isomorphic spaces. So it is customary to just always pick the matrix with only +1 and -1 as entries.

Intuitive definition: real group of rotations + reflections.

Mathematical definition that most directly represents this: the orthogonal group is the group of all matrices that preserve the dot product.

The degree of some algebraic structure is some parameter that describes the structure. There is no universal definition valid for all structures, it is a per structure type thing.

This is particularly useful when talking about structures with an infinite number of elements, but it is sometimes also used for finite structures.

Examples:

Demo under: nodejs/sequelize/raw/many_to_many.js.

NO way in the SQL standard apparently, but you'd hope that implementation status would be similar to UPDATE with JOIN, but not even!

The problem of deletionism is that it removes users' confidence that their precious data will be safe. It's almost like having a database that constantly resets itself. Who will be willing to post on a website that deletes the content they created for free half of the time thus wasting people's precious time?

The Klein-Gordon equation directly uses a more naive relativistic energy guess of $p^2+m^2$ squared.

But since this is quantum mechanics, we feel like making $p$ into the "momentum operator", just like in the Schrödinger equation.

But we don't really know how to apply the momentum operator twice, because it is a gradient, so the first application goes from a scalar field to the vector field, and the second one...

So we just cheat and try to use the laplace operator instead because there's some squares on it:

But then, we have to avoid taking the square root to reach a first derivative in time, because we don't know how to take the square root of that operator expression.

So the Klein-Gordon equation just takes the approach of using this squared Hamiltonian instead.

Since it is a Hamiltonian, and comparing it to the Schrödinger equation which looks like:taking the Hamiltonian twice leads to:

We can contrast this with the Dirac equation, which instead attempts to explicitly construct an operator which squared coincides with the relativistic formula: derivation of the Dirac equation.

Where derivation == "intuitive routes", since a "law of physics" cannot be derived, only observed right or wrong.

TODO also comment on why are complex numbers used in the Schrodinger equation?.

Some approaches:

The derivative of a function gives its slope at a point.

More precisely, it give sthe inclination of a tangent line that passes through that point.

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.

Name origin: likely because it "determines" if a matrix is invertible or not, as a matrix is invertible iff determinant is not zero.