Mass and spin of the particle are used in classification of elementary particles. The mass is defined to be a Lorentz invariant quantity. On the other hand, the spin is a spacelike 4-vector and cannot be defined as an invariant quantity.
My question is, what would be a convenient definition of a relativistic spin 3-vector? As is known, 3-vectors get contracted/dilated under Lorentz transformations. So, is the 3-spin defined to be equal to the rest frame 3-spin, or do we allow it to contract/dilate? It seems to me that the first option is generally used, especially when considering Thomas precession and similar effects. Although, I haven't seen any relevant discussion in textbooks on this topic.