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The Group SU(2), Weak Force Symmetry

Posted by doug
The group of unitary quaternions is the symmetry underlying the weak force of radioactive decay. Who would have thought the symmetry looks like this?
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.
q_graph -dir vp -out group_SU2 -loop 0 -box 1.1 -command 'q_random_n_11 50000 | q_vector | q_exp'
youtube embed: 

[tex]exp(A - A^*)\in SU(2)[/tex]