Pauli–Lubanski pseudovector

In physics, specifically in relativistic quantum mechanics and quantum field theory, the Pauli–Lubanski pseudovector named after Wolfgang Pauli and Józef Lubański is an operator defined from the momentum and angular momentum, used in the quantum-relativistic description of angular momentum.

It describes the spin states of moving particles. It is the generator of the little group of the Poincaré group, that is the maximal subgroup (with four generators) leaving the eigenvalues of the four-momentum vector P_μ invariant.

It is usually denoted by W (or less often by S) and defined by:

${\displaystyle W_{\mu }{\stackrel {\mathrm {def} }{=}}~{\tfrac {1}{2}}\varepsilon _{\mu \nu \rho \sigma }J^{\nu \rho }P^{\sigma },}$

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