Does spin change under Lorentz boosts?

[QuantumCosmo]

Hi,
I was wondering if the spin of a particle changed under Lorentz boosts. I think what it comes down to is if S^2 commutes with the generators of Lorentz boosts (the components of S only generate the rotations of the spinor I think). I think that should be true (an electron should always be a spin 1/2 particle in every coordinate system). So I hope S^2 commutes with those generators?
The next question is: What about the spin direction? Take S_z for example. Does S_z commute with the generators of Lorentz boosts? If an electron has spin up in one coordinate system, does it have spin up in all others too?
(For rotations that is obviously not true. If we rotate the system around the x axis, a particle that was previously characterized by spin in the z direction will now have a component in the y direction too because S_z and S_x don't commute)
Thank you,
QuantumCosmo

 

[tom.stoer]

Spin orientation does change, but spin 1/2 which should better read S² = 1/2 * (1/2 + 1) = 3/4 is valid in all reference frames. This due the fact that the S² is something like the second Casimir (p²=m² is the first) and therefore commutes with all Lorentz generators. More exactly, one has to use the Pauli-Lubanski operator W instead of S; for W one finds W² = -m² s (s+1) which is a c-number.

http://en.wikipedia.org/wiki/Pauli-lubanski_pseudovector

 

[Bill_K]

Note that it is not straightforward to interpret the Pauli-Lubanski vector as a spin vector when the particle is moving. W_μ is orthogonal to P^μ in the four-dimensional sense, so for a moving particle W_μ will have a time component. And of course the three space components (W_x, W_y, W_z) taken by themselves won't have the expected norm.