- #1
QuantumCosmo
- 29
- 0
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
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