He is so far the best professor providing a holistic and intuitive way to grasp high level physics.

Concepts of symmetry, there is static symmetry and dynamic symmetry. What is static and what is dynamic symmetry? static symmetry is like transform/rotate a triangle simple case, while dynamic symmetry refers to Lagragian transforming, more abstract also more useful. the former is time-independent while the latter is overtime.

More importantly is to grasp various types of transformation: global and local, discrete and continuous, compact and infinite, initial and spacetime…

degeneracy. In the context of high-level physics, particularly quantum mechanics and statistical mechanics, “degeneracy” refers to the condition where different quantum states of a system have the same energy. In other words, degeneracy is the existence of multiple distinct states of a system that all have the same energy level. In the context of transformation of a square shapre, there are four-fold no degeneracy, two-fold(0 and 90degree) degeneracy, and one-fold, extreme degeneracy scenarios.

Transformation is super important and what physicists are dedicated to achieve is the invariance upon transformation.

How do we get r twirl? it is r transformed (producted) by metric g, where g is symmetrical g^T = g

Then prof.Flournoy deduced the rotation transformation R^TR = identity

Next onto special relativity from group/transformation perspective, a brand new perspective that is given the metric g, to find the group A in A^TgA = g.

The Minkovski spacetime metric is given a special sign eita instead of general metric g. And there are three rotations and three boosts.