For ˜µ=δ ˜F /δρ, the chain rule gives the exact identity⟨ψ aℓJ ,˜µ⟩=∂ aℓJ ˜F

The deterministic term⟨ψ aℓJ ,˜µ[ρ]⟩ Instead of performing the full integral, since the deterministic term is equilibrium-like (variational), we can take a shortcut