Ciro Santilli @cirosantilli 40

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.

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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.

Like the rest of the Standard Model Lagrangian, this can be split into two parts:

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

Lit: fish timber question answer.

On Baidu Baike: baike.baidu.com/item/渔樵问答/336905

The dialog is also known as allegory for an incredibly deep philosophical discussion between an idealized wise woodcutter and a fisherman, e.g. mentioned at: www2.kenyon.edu/Depts/Religion/Fac/Adler/Writings/Fisherman%20and%20Woodcutter.pdf

This song is just too slow for Ciro Santilli to make much out of it.

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Reaches 2 mK^[ref]. youtu.be/upw9nkjawdy?t=487 from Video "Building a quantum computer with superconducting qubits by Daniel Sank (2019)" mentions that 15 mK are widely available.

Used for example in some times of quantum computers, notably superconducting quantum computers. As mentioned at: youtu.be/uPw9nkJAwDY?t=487, in that case we need to go so low to reduce thermal noise.

Ideally can be thought of as a one-way ticket gate that only lets electrons go in one direction with zero resistance! Real devices do have imperfections however, so there is some resistance.

First they were made out of vacuum tubes, but later semiconductor diodes were invented and became much more widespread.