Manuscript XIII-D@1 · XIII-D.tex · section · bab69024

D5: the copied witness on a parameter commutator

D5: the copied witness on a parameter commutator · lines 1019–1043

XIII-D@1#eq:B-theta

Use the copied free-shell configuration

m = 0, ψ = t^{2} + (x^{1})^{2}, γ = ψ η, ϕ = ψ, b = (- 2 t, 2 x^{1}, 0, 0), c = c ˉ = 0,

denoted $u_{*}$ . Its shell membership, compact realization, causal-plateau hypothesis, and evaluated sign are those of XII-F.

Set

I = \int f (t, x) \int_{0}^{t} (t - s)^{2} h (s)^{2} d s d^{4} x .

The copied witness gives $I > 0$ and

B_{θ} (u_{*}) = - 8 I < 0.

No retarded cylinder calculation is repeated.

Displayed formulas in this passage

XIII-D@1#eq:B-theta · line 1038
$B_{θ} (u_{*}) = - 8 I < 0.$
unlabeled · line 1022
$m = 0, ψ = t^{2} + (x^{1})^{2}, γ = ψ η, ϕ = ψ, b = (- 2 t, 2 x^{1}, 0, 0), c = c ˉ = 0,$
unlabeled · line 1033
$I = \int f (t, x) \int_{0}^{t} (t - s)^{2} h (s)^{2} d s d^{4} x .$