Manuscript II@2 · II.tex · section · 50d64def

Original pivot columns

Complete matrix encoding and the finite certificate › Original pivot columns · lines 1475–1503

II@2#eq:labels, II@2#eq:pivot-actions

Choose

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

and

ℓ_{a} = ((1, 1, 2, 2), P_{0}), ℓ_{b} = ((2, 2, 1, 1), P_{0}) .

They correspond to

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} .

Here $h^{I}$ without indices is the Lorentz trace.

Displayed formulas in this passage

II@2#eq:labels · line 1482
$ℓ_{a} = ((1, 1, 2, 2), P_{0}), ℓ_{b} = ((2, 2, 1, 1), P_{0}) .$
II@2#eq:pivot-actions · line 1488
$O_{a} O_{b} = \int d^{4} x (\partial_{λ} h^{1}) (\partial^{λ} h^{1}_{μν}) h^{2 μ ρ} h^{2 ν}_{ρ}, = \int d^{4} x (\partial_{λ} h^{2}) (\partial^{λ} h^{2}_{μν}) h^{1 μ ρ} h^{1 ν}_{ρ} .$
unlabeled · line 1478
$P_{0} = {{1, 2}, {3, 4}, {5, 7}, {6, 9}, {8, 10}}$