Manuscript Em01-G@5 · Em01-G-v5.tex · proposition · 3fbfe951

Proposition: Exhaustive supported plateau inventory

Supported output-plateau inverse-quadratic inventory · lines 2592–2624 · proof included or linked

Em01-G@5#prop:plateau-inventory, Em01-G@5#eq:plateau-inventory

For tests supported in an output plateau,

A_{- 2}^{supp} (Φ) = \frac{1}{32 π ^{2}} \int \frac{1}{β} {\frac{M _{2}}{2} I, J, ζ, j j = 1, 2, ∣ ζ ∣ + j \leq 3 \sum (- 1)^{∣ ζ ∣ + j} j c_{ζ, j}^{I, J} (ϑ, 0, 0) (e^{I})^{μν} ℓ_{μ} H_{ζ, j, J}^{ν} + \frac{m ^{2} M _{2}}{2} I, J, ζ ∣ ζ ∣ \leq 1 \sum (- 1)^{∣ ζ ∣} ϑ_{I} c_{ζ, 2}^{I, J} (ϑ, 0, 0) (\partial_{r}^{ζ} Φ_{J}) (w_{0}) + I, J, ζ, μ, ν ∣ ζ ∣ \leq 1 \sum (e^{I})^{μν} L_{μ} [B_{ζ, I, J}^{ν}]} d ϑ .

Proof. Inverse-quadratic supported order consists exactly of $q = 2, n = 0$ and $q = 3, n = 1$ in (eq:supported-coefficients). These are respectively the $b = 1$ kinetic terms, the $b = 2$ mass terms, and the first correction of the $b = 2$ kinetic terms. Insert the preceding scalar contact formulas with the signs and binomial factors in (eq:supported-amplitudes).

Displayed formulas in this passage

Em01-G@5#eq:plateau-inventory · line 2595
$A_{- 2}^{supp} (Φ) = \frac{1}{32 π ^{2}} \int \frac{1}{β} {\frac{M _{2}}{2} I, J, ζ, j j = 1, 2, ∣ ζ ∣ + j \leq 3 \sum (- 1)^{∣ ζ ∣ + j} j c_{ζ, j}^{I, J} (ϑ, 0, 0) (e^{I})^{μν} ℓ_{μ} H_{ζ, j, J}^{ν} + \frac{m ^{2} M _{2}}{2} I, J, ζ ∣ ζ ∣ \leq 1 \sum (- 1)^{∣ ζ ∣} ϑ_{I} c_{ζ, 2}^{I, J} (ϑ, 0, 0) (\partial_{r}^{ζ} Φ_{J}) (w_{0}) + I, J, ζ, μ, ν ∣ ζ ∣ \leq 1 \sum (e^{I})^{μν} L_{μ} [B_{ζ, I, J}^{ν}]} d ϑ .$

Proposition: Exhaustive supported plateau inventory

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