Manuscript XVI-J@1 · XVI-J.tex · definition · 6c1f306d

Definition: Selected extension

An operational extension prescription › The selected extension · lines 1218–1232

XVI-J@1#def:extension, XVI-J@1#eq:extension

The prescription $R = R_{ϖ}$ is

⟨ q ˉ^{R_{ϖ}}, ψ ⟩ = T_{0} (W_{ϖ} ψ) = \int_{0}^{\infty} \frac{d ρ}{ρ} ⟨ A, ψ (ρ \cdot) - ψ (0) ϖ (ρ \cdot) ⟩

for every compact smooth test $ψ$ .

Displayed formulas in this passage

XVI-J@1#eq:extension · line 1221
$⟨ q ˉ^{R_{ϖ}}, ψ ⟩ = T_{0} (W_{ϖ} ψ) = \int_{0}^{\infty} \frac{d ρ}{ρ} ⟨ A, ψ (ρ \cdot) - ψ (0) ϖ (ρ \cdot) ⟩$