Then the corresponding space-time vector of the first kind ω[Φ, ψ] vanishes identically owing to equations 9) and 53)
for ω[Φ.ψ] = -(ωψ)Φ + (ωΦ)ψ
Let us now take the vector of the 1st kind
(57) Ω = iω[Φψ]*
with the components
Ω₁ = -i | ω₂ ω₃ ω₄ |
| Φ₂ Φ₃ Φ₄ |
| ψ₂ ψ₃ ψ₄ |, etc.
Then by applying rule (45), we have
(58) [Φ.ψ] = i[ωΩ]*