Dear Hou Yau,
I'm really glad you bring up those issues. It also shows that a 10 page essay is really not enough to explain the intricacies.
You're right, in relativity the world line is straight. These is no controversy here, provided that one uses discrete time intervals and particle displacement for the description of helical motion. Define dt_0 as the period of the stationary particle (quantum loop), dt as the period of a single helical cycle for the electron in motion and dx as the distance traveled by the helical path of the electron as measured along the helix axis. Then one can show that (c*dt_0)sup 2 = (c*dt)sup2 - (dx)sup 2 (where c is the speed of light, sup2 indicates the square operation), see report 2 on my website). In other words, discrete quantum behavior and relativity co-exist in the helical motion of the electron.
I haven't considered the relevance of the Pauli matrices in relation to helical motion. It could be that they are applicable to the averaged behavior of the electron as exhibited along the helix axis.
BB