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Manuscript IX-C-ST@1 · IX-C-ST.tex · section · 892f50c4

Concrete relations and evaluated scalar descent

Concrete relations and evaluated scalar descent · lines 1432–1450

IX-C-ST@1#eq:Prelationkernel

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Let $J^{μ}_{α β} (x, z)$ be the supported kernel of $L$ , and let $e_{00}^{α β} h_{α β} = h_{00}$ . Define

P [v] (x, z_{1}, z_{2}, z_{3}) = Sym_{(z_{j}, α_{j}, β_{j})} \partial_{x^{μ}} [v (x, z_{2}) J^{μ}_{α_{1} β_{1}} (x, z_{1}) δ (z_{2} - z_{3}) e_{00}^{α_{2} β_{2}} e_{00}^{α_{3} β_{3}}] .

Symmetrization is averaging over the three metric slots.

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IX-C-ST@1#eq:Prelationkernel · line 1437
$P [v] (x, z_{1}, z_{2}, z_{3}) = Sym_{(z_{j}, α_{j}, β_{j})} \partial_{x^{μ}} [v (x, z_{2}) J^{μ}_{α_{1} β_{1}} (x, z_{1}) δ (z_{2} - z_{3}) e_{00}^{α_{2} β_{2}} e_{00}^{α_{3} β_{3}}] .$

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