Ciro Santilli @cirosantilli  40

Surprisingly, it can also become a superfluid even though each atom is a fermion! This is because of Cooper pair formation, just like in superconductors, but the transition happens at lower temperatures than superfluid helium-4, which is a boson.

aps.org/publications/apsnews/202110/history.cfm: October 1972: Publication of Discovery of Superfluid Helium-3 contains comments on the seminal paper and a graph which we must steal.

Also sometimes called helium II, in contrast to helium I, which is the non-superfluid liquid helium phase.

This is true. The level of competition in university entry exams in Asia in insane in the early 21st century compared to the West.

This is actually both good and bad. Good because it selects some very good exam passers. And bad because it selects some very good exam passers.

Lie Groups, Physics, and Geometry by Robert Gilmore (2008) 7.2 "The covering problem" gives some amazing intuition on the subject as usual.

The most important example is perhaps $SO(3)$ and $SU(2)$, both of which have the same Lie algebra, but are not isomorphic.

Derivation from older alphabets: en.wikipedia.org/w/index.php?title=History_of_the_Latin_script&oldid=1042752124#Derivation_from_Egyptian_hieroglyphs

Show up when solving the Laplace's equation on spherical coordinates by separation of variables, which leads to the differential equation shown at: en.wikipedia.org/w/index.php?title=Legendre_polynomials&oldid=1018881414#Definition_via_differential_equation.

Generalization of Laplace's equation where the value is not necessarily 0.

A solution to Laplace's equation.

Basically: S.

The variables of the Lagrangian, e.g. the angles of a double pendulum. From that example it is clear that these variables don't need to be simple things like cartesian coordinates or polar coordinates (although these tend to be the overwhelming majority of simple case encountered): any way to describe the system is perfectly valid.

In quantum field theory, those variables are actually fields.