The Pauli-Lubanski pseudovector is an important concept in theoretical physics, particularly in the context of relativistic quantum mechanics and the study of angular momentum and symmetry in particle physics. It serves as a relativistic generalization of angular momentum. In the realm of special relativity, the total angular momentum \( J^{\mu} \) of a system can be expressed in terms of the orbital angular momentum and the intrinsic spin of the particles involved.
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The Pauli-Lubanski pseudovector is , up to an overall sign convention. Its square is a Casimir of the Poincare algebra and measures spin in a massive irreducible representation.