One of perks of PhD of quantum physics is that quaternions get mundane, vide https://en.wikipedia.org/wiki/Pauli_matrices https://en.wikipedia.org/wiki/Pauli_ma

One of perks of PhD of quantum physics is that quaternions get mundane, vide https://en.wikipedia.org/wiki/Pauli_matrices https://en.wikipedia.org/wiki/Pauli_matrices. SU(2) is everywhere (normalized quaternions). These are are more common than regular rotations of 3D space, O(3). Because SU(2) we get a lot of interesting phenomena, including that there are two types of particles, bosons and fermions. We get some interesting phenomena that only rotating by 720deg (two full rotations) bring back to the initial state. And I am not talking only about USB-A, but about spinors (https://en.wikipedia.org/wiki/Spinor https://en.wikipedia.org/wiki/Spinor) - there are some party tricks around that (vide https://www.reddit.com/r/physicsmemes/comments/181oldw/a_german_demonstrating_720_degrees_symmetry_for/ https://www.reddit.com/r/physicsmemes/comments/181oldw/a_ger...).