Spin-one Cartesian basis
= Spin-one Cartesian basis
The spin-one Cartesian basis $|x\rangle,|y\rangle,|z\rangle$ transforms as a three-dimensional vector under rotations. In its two-site tensor square, the scalar, antisymmetric, and symmetric traceless subspaces are respectively the total-spin $0$, $1$, and $2$ sectors.