Spatial rotation vector field (${\Omega }_{ij}=x_i{\partial }_j-x_j{\partial }_i$)

The vector field ${\Omega }_{ij}=x_i{\partial }_j-x_j{\partial }_i$ is an infinitesimal spatial rotation. It commutes with the flat d'Alembert operator and supplies angular derivatives in the Klainerman-Sobolev inequality.