# The Group SU(2), Weak Force Symmetry

summary:

The group of unitary quaternions is the symmetry underlying the weak force of radioactive decay. Who would have thought the symmetry looks like this?
description:

If one takes the vector part of a quaternion and takes the exponential, the norm is always equal to 1. The animation starts out at 8 points, those for exp(0, +/-1, +/-1, +/-1). These points grow into each other until they form a sphere. That sphere then shrinks to the point (1, 0, 0, 0), the furthest into the future the exponential can reach.
command:

q_graph -dir vp -out group_SU2 -loop 0 -box 1.1 -command 'q_random_n_11 50000 | q_vector | q_exp'

youtube link:

The Group SU(2)
iPod downloads:

equation:

sage notebook:

The Group SU(2)
numbers: