- #1
Heirot
- 151
- 0
I have a problem understanding the Lorentz transformation of the spin. The spin 4-vector is defined in the rest frame of the particle as
[itex]s^{\mu} = (0, \vec{s})[/itex]
and then boosted in any other frame according to
[itex]s'^{\mu} = (\gamma \vec{\beta} \cdot \vec{s}, \vec{s} + \frac{\gamma^2}{1+\gamma}(\vec{\beta} \cdot \vec{s}) \vec{\beta})[/itex]
I have a couple of question concerning this.
1) How can spin transform as a 4-vector, when the angular momentum transforms as a 4-tensor with two indices?
2) How can I interpret the zeroth component of the spin 4-vector in an arbitrary inertial reference frame?
3) It is often said that one cannot separate the total angular momentum J into the orbital angular momentum L and spin S in a covariant way. In light of this (which I do not completely understand), what to make of this spin 4-vector?
Thank you!
[itex]s^{\mu} = (0, \vec{s})[/itex]
and then boosted in any other frame according to
[itex]s'^{\mu} = (\gamma \vec{\beta} \cdot \vec{s}, \vec{s} + \frac{\gamma^2}{1+\gamma}(\vec{\beta} \cdot \vec{s}) \vec{\beta})[/itex]
I have a couple of question concerning this.
1) How can spin transform as a 4-vector, when the angular momentum transforms as a 4-tensor with two indices?
2) How can I interpret the zeroth component of the spin 4-vector in an arbitrary inertial reference frame?
3) It is often said that one cannot separate the total angular momentum J into the orbital angular momentum L and spin S in a covariant way. In light of this (which I do not completely understand), what to make of this spin 4-vector?
Thank you!