James R, I think with my equations the correlation between relativity or Lorentz Transformations with the spin of a particle can be better understood.
Consider a massive, spinning particle is generated through pair production from the mass-less particle photon. If no force is applied to this particle, it will remain at rest(v=0). Though at rest, the particle will be spinning at its intrinsic spin. Say mass of the particle is m, its radius is r, moment of Inertia is I, angular momentum L and angular speed is w. If the particle is in its intrinsic spin, its angular momentum will be conserved. So, L=Iw. Here I can be written as I=mr^2k, where k is some constant. So, L=Iw=mr^2kw or m=L/r^2wk. As k is constant, we can write m=(L/k)/r^2w. From this equation we can see that, concept of mass generates from conservation of angular momentum. This mass m can vary with r and w. As r and w increases, mass will decrease and as r and w decrease, mass will increase.
Even if the particle is at rest, it will be in its intrinsic spin. So, the particle will be having a tangential speed rw. Now if the particle is moved at a speed v, the maximum tangential speed will v+rw. If the v is kept on increasing, v+rw may exceed c, which is not permitted. So the particle will try to reduce its tangential speed by reducing r and w. As r and w decrease, from the mass equation we can see that, its mass will increase. Thus as v increases, its mass will increase and its radius and angular speed will reduce. So, relativity or Lorentz Transformations can be linked with the spin of a particle.