Since the angular momentum vector [itex]\mathbf{J}[/itex] is just a 3-vector, it transforms non-covariantly under Lorentz transformations -- more specifically, boosts generated by [itex]\mathbf{K}[/itex]. Indeed, the commutator reads [itex][J_i,\,K_j]=i\epsilon_{ijk}J_k[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Under a finite boost, I find the angular momentum vector gets mixed up with the 'boost vector'

[tex]\mathbf{J}\rightarrow\gamma\left[\mathbf{J}-\left(\frac{\gamma}{\gamma+1}(\mathbf{\beta}\cdot \mathbf{J})\mathbf{\beta}-\mathbf{\beta}\times\mathbf{K}\right)\right][/tex]

(c.f.the Lorentz transformation of the electric field). How do I interpret this result? In which direction does the new angular momentum vector point? It depends on the boost vector?

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# Boosting the angular momentum vector

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