Manuscript XVI-K@1 · XVI-K.tex · definition · aa7553bb

Definition: Source-decorated coefficients

The selected source and differentiated graph kernels › Coefficients and unordered placements · lines 854–871

XVI-K@1#def:a, XVI-K@1#eq:Kpq, XVI-K@1#eq:apq

For $∣ p ∣ + ∣ q ∣ \leq 2$ , set

K^{μν}_{pq} (y, w; h) a^{μν}_{pq} (y, w; h) = i, j = 0 \sum^{9} L^{pq}_{ij} (w; h) s^{μν} (Z_{i}, Z_{j}; Σ (y)), = (- 1)^{∣ p ∣ + ∣ q ∣} χ_{I} (w) K^{μν}_{pq} (y, w; h) .

The interaction switch appears exactly once in $a_{pq}$ .

Displayed formulas in this passage

XVI-K@1#eq:Kpq · line 857
$K^{μν}_{pq} (y, w; h) a^{μν}_{pq} (y, w; h) = i, j = 0 \sum^{9} L^{pq}_{ij} (w; h) s^{μν} (Z_{i}, Z_{j}; Σ (y)), = (- 1)^{∣ p ∣ + ∣ q ∣} χ_{I} (w) K^{μν}_{pq} (y, w; h) .$
XVI-K@1#eq:apq · line 857
$K^{μν}_{pq} (y, w; h) a^{μν}_{pq} (y, w; h) = i, j = 0 \sum^{9} L^{pq}_{ij} (w; h) s^{μν} (Z_{i}, Z_{j}; Σ (y)), = (- 1)^{∣ p ∣ + ∣ q ∣} χ_{I} (w) K^{μν}_{pq} (y, w; h) .$