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

The evaluator

Complete contacts and the exact three-row certificate › The evaluator · lines 818–844

II-B@1#eq:evaluator

For covariant momenta $p, q$ , define

Contr_{P} (p, q; e_{1}, e_{2}, e_{3}, e_{4}) = λ_{1}, \dots, λ_{10} = 0 \sum^{3} p_{λ_{1}} q_{λ_{2}} r = 1 \prod^{4} (e_{r})_{λ_{2 r + 1} λ_{2 r + 2}} {u, v} \in P \prod η^{λ_{u} λ_{v}} .

The response of a raw contact is

n_{I, P} (β) = - σ \in S_{4} \sum (r = 1 \prod^{4} δ_{I_{r}, J_{σ (r)}}) Contr_{P} (k_{σ (1)}, k_{σ (2)}; e_{σ (1)}, e_{σ (2)}, e_{σ (3)}, e_{σ (4)}) .

One $e_{i}$ is $G$ . Substitution of four distinctly labelled waves into (eq:raw) and extraction of their product gives this formula. The two derivatives contribute $i^{2} = - 1$ .

Displayed formulas in this passage

II-B@1#eq:evaluator · line 830
$n_{I, P} (β) = - σ \in S_{4} \sum (r = 1 \prod^{4} δ_{I_{r}, J_{σ (r)}}) Contr_{P} (k_{σ (1)}, k_{σ (2)}; e_{σ (1)}, e_{σ (2)}, e_{σ (3)}, e_{σ (4)}) .$
unlabeled · line 821
$Contr_{P} (p, q; e_{1}, e_{2}, e_{3}, e_{4}) = λ_{1}, \dots, λ_{10} = 0 \sum^{3} p_{λ_{1}} q_{λ_{2}} r = 1 \prod^{4} (e_{r})_{λ_{2 r + 1} λ_{2 r + 2}} {u, v} \in P \prod η^{λ_{u} λ_{v}} .$