Part 6/9:
Spinners as Two-Component Complex Vectors
Spinners can be defined as two-component complex vectors that are manipulated by SU(2) matrices. They encapsulate the behavior of particles in a way traditional algebraic methods cannot. This highlights how SU(2) matrices relate to quantum mechanics, specifically the wave function of electrons, establishing spinners' central role in relativistic quantum physics.
The Double Cover Relationship
The two-to-one relationship between SU(2) and SO(3) elucidates how spinners offer crucial insights into the underlying mechanics of rotations—where a 360-degree rotation in three-dimensional space results in the same orientation as a rotation of 720 degrees in the realm of spinners.