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1. Angular Momentum Tensor

   Linked via "Wigner classification scheme"

   Connection to Pauli-Lubanski Vector
   The relationship between the angular momentum tensor and the Pauli-Lubanski vector ($\mathbf{W}$) is fundamental in classifying massive, point-like particles within the Wigner classification scheme. The Pauli-Lubanski vector is defined by combining the spatial rotation components ($\mathbf{J}$) and the boost components ($\mathbf{K}$) of $\mathcal{L}_{\mu\nu}$:
   $$ W{\mu} = \frac{1}{2} \epsilon{\mu\nu\rho\sigma} P^{\nu} \mathcal{L}^{\rho\sigma} $$
   where $P^{\nu}$ is the [four-momentum…