Manuscript X-E-ST@1 · X-E-ST.tex · section · 44614221

Three scalar slots, not just a two-point slogan

E4: the isolated matter-induced tree › Three scalar slots, not just a two-point slogan · lines 1537–1560

X-E-ST@1#eq:t3

Define the polarized trace-reversed stress

T_{α β} (v, w) = \frac{1}{2} (T_{tr, α β} [v + w] - T_{tr, α β} [v] - T_{tr, α β} [w]), T_{tr} = P_{tr} T_{0} .

Thus $T (u, u) = P_{tr} T_{0} [u]$ . It is a constant-coefficient local bilinear differential expression, including its mass term.

Define a symmetric cubic kernel $t_{3}$ by

⟨ t_{3}, u_{1} \otimes u_{2} \otimes u_{3} ⟩ = \frac{1}{3} cyc \sum ⟨ t^{α β} (x, y), u_{1} (x) T_{α β} (u_{2}, u_{3}) (y) ⟩ .

Displayed formulas in this passage

X-E-ST@1#eq:t3 · line 1553
$⟨ t_{3}, u_{1} \otimes u_{2} \otimes u_{3} ⟩ = \frac{1}{3} cyc \sum ⟨ t^{α β} (x, y), u_{1} (x) T_{α β} (u_{2}, u_{3}) (y) ⟩ .$
unlabeled · line 1540
$T_{α β} (v, w) = \frac{1}{2} (T_{tr, α β} [v + w] - T_{tr, α β} [v] - T_{tr, α β} [w]), T_{tr} = P_{tr} T_{0} .$