Manuscript II-B@1 · II-B-v1.tex · section · bfd2eb3c

Original pivots, rank, fit, and kernels

Complete contacts and the exact three-row certificate › Original pivots, rank, fit, and kernels · lines 1061–1080

Choose

P_{0} = {{1, 2}, {3, 4}, {5, 7}, {6, 9}, {8, 10}} .

Let $ℓ_{a} = ((1, 1, 2, 2), P_{0})$ and $ℓ_{b} = ((2, 2, 1, 1), P_{0})$ . Their actions are

O_{a} O_{b} = \int d^{4} x (\partial_{λ} h^{1}) (\partial^{λ} h^{1}_{μν}) h^{2 μ ρ} h^{2 ν}_{ρ}, = \int d^{4} x (\partial_{λ} h^{2}) (\partial^{λ} h^{2}_{μν}) h^{1 μ ρ} h^{1 ν}_{ρ},

where an unindexed $h^{I}$ is the Lorentz trace.

Displayed formulas in this passage

unlabeled · line 1069
$O_{a} O_{b} = \int d^{4} x (\partial_{λ} h^{1}) (\partial^{λ} h^{1}_{μν}) h^{2 μ ρ} h^{2 ν}_{ρ}, = \int d^{4} x (\partial_{λ} h^{2}) (\partial^{λ} h^{2}_{μν}) h^{1 μ ρ} h^{1 ν}_{ρ},$
unlabeled · line 1064
$P_{0} = {{1, 2}, {3, 4}, {5, 7}, {6, 9}, {8, 10}} .$