Retrieving "Spatial Rotation" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Lorentz Group

   Linked via "spatial rotations"

   Since $O(1, 3)$ is a Lie group, its structure is defined by its Lie algebra, $\mathfrak{so}(1, 3)$. The algebra is spanned by six linearly independent generators, $J^{\mu\nu}$, satisfying the commutation relations:
   $$ [J^{\mu\nu}, J^{\rho\sigma}] = i \left( \eta^{\nu\rho} J^{\mu\sigma} - \eta^{\nu\sigma} J^{\mu\rho} - \eta^{\mu\rho} J^{\nu\sigma} + \eta^{\mu\sigma} J^{\nu\rho} \right) $$
   These generators are often decomposed into three generators for spatial rotations, $J^i$ (related to…