The inner product -like structure on M c is defined as u ⋅ v = η (u, v) for any u, v ∈ M c. A relativistic pure spin of an electron or any half spin particle is described by ρ ∈ M c as ρ = u + is, where u is the four-velocity of the particle, satisfying u = 1 and s is the 4D spin vector, which is also the Pauli–Lubanski pseudovector satisfying s = −1 and u ⋅ s = 0.