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Recall that the value and sight of $\mathbf{r} \times \mathbf{p}$ angular momentum depends on the point around which you chose to measure it. A free particle can (indeed, does) have angular momentum around any and all points relative which it is moving and has a non-zero impact parameters. But, frankly, that's not a very interesting statement.


For massive spinors "right-handed" and "left-handed" chirality isn't tied so much to true rotations, as to the casting of Lorentz transformations as "space-time rotations". In this case, a very popular short answer to the conceptual question is that Lorentz transformations "rotate" $(1/2, 0)$-spinors one way in space-time, and $(0, 1/2)$-spinors the opposite ...

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