Manuscript XIII-B@1 · XIII-B.tex · section · b8a5c0f5

The response branches and the overlap

B3a: the constructed one-line causal composition › The response branches and the overlap · lines 836–852

XIII-B@1#eq:tree-branches

Substituting (eq:vertex-derivatives) and (eq:action-inverse) gives

R_{1}^{(0)} = ⟨ O^{'}_{γ}, r_{g} [ϕ] ⟩ + ⟨ O^{'}_{ϕ}, p_{1} [γ; ϕ] ⟩, p_{1} [γ; ϕ] = - E_{m}^{R} V_{1, g} [γ] ϕ .

Both the metric inverse coefficient $- 1$ and the scalar Hessian sign have been retained.

Displayed formulas in this passage

XIII-B@1#eq:tree-branches · line 840
$R_{1}^{(0)} = ⟨ O^{'}_{γ}, r_{g} [ϕ] ⟩ + ⟨ O^{'}_{ϕ}, p_{1} [γ; ϕ] ⟩, p_{1} [γ; ϕ] = - E_{m}^{R} V_{1, g} [γ] ϕ .$