Manuscript XVI-P@p23 · XVI-P.tex · section · 9b0037a7

Gate 2: normalized D11 — prefactor Constructed; tensor Constructed

Massless scalar matter-loop subsector (o70-sync) › Gate 2: normalized D11 — prefactor Constructed; tensor Constructed · lines 1686–1697

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Route A (Wick) independently yields

lo g Z_{bubble} = - \frac{κ ^{2}}{8} \int h T h, Γ_{1, matter} = - i lo g Z, Π_{bubble} = \frac{i κ ^{2}}{4} V V (C C + C C) .

Route B expands $lo g Z = - \frac{1}{2} Tr lo g H$ to $(- κ^{2} /4) Tr (D_{F} H_{1} D_{F} H_{1})$ . Symmetry of $a_{1}$ gives $comb_{B} = \frac{1}{2}$ (Constructed — not unresolved) and $Π_{B} = i κ^{2} /4 T$ . Tensor witness $T_{0000} = 24 A^{2} / r^{8}$ at $z = (0, r, 0, 0)$ .

Displayed formulas in this passage

unlabeled · line 1688
$lo g Z_{bubble} = - \frac{κ ^{2}}{8} \int h T h, Γ_{1, matter} = - i lo g Z, Π_{bubble} = \frac{i κ ^{2}}{4} V V (C C + C C) .$