Manuscript IX-Free@1 · IX-Free.tex · section · 33b20e96

F7: four-order coherence, conditional on the missing maps

F7: four-order coherence, conditional on the missing maps · lines 1274–1305

IX-Free@1#eq:AL, IX-Free@1#eq:AR

Write

P_{L} = A W, Q_{L} = Q_{f, g}, P_{R} = W C, Q_{R} = Q^{R}_{g, f^{'}} .

Under the selected contraction-degree prescription, a completed candidate would have

A_{L} = A_{R} = P_{L} C + ℏ (L_{1} (P_{L}, C) + Q_{L} C) + ℏ^{2} (L_{2} (P_{L}, C) + L_{1} (Q_{L}, C)) + ℏ^{3} L_{2} (Q_{L}, C), A P_{R} + ℏ (R_{1} (A, P_{R}) + A Q_{R}) + ℏ^{2} (R_{2} (A, P_{R}) + R_{1} (A, Q_{R})) + ℏ^{3} R_{2} (A, Q_{R}) .

The residual degrees are $6, 4, 2, 0$ .

The absence of a third contraction against a degree-two sharp factor is the selected graph prescription. It is not a theorem forbidding every possible additional contact term.

Displayed formulas in this passage

IX-Free@1#eq:AL · line 1284
$A_{L} = A_{R} = P_{L} C + ℏ (L_{1} (P_{L}, C) + Q_{L} C) + ℏ^{2} (L_{2} (P_{L}, C) + L_{1} (Q_{L}, C)) + ℏ^{3} L_{2} (Q_{L}, C), A P_{R} + ℏ (R_{1} (A, P_{R}) + A Q_{R}) + ℏ^{2} (R_{2} (A, P_{R}) + R_{1} (A, Q_{R})) + ℏ^{3} R_{2} (A, Q_{R}) .$
IX-Free@1#eq:AR · line 1284
$A_{L} = A_{R} = P_{L} C + ℏ (L_{1} (P_{L}, C) + Q_{L} C) + ℏ^{2} (L_{2} (P_{L}, C) + L_{1} (Q_{L}, C)) + ℏ^{3} L_{2} (Q_{L}, C), A P_{R} + ℏ (R_{1} (A, P_{R}) + A Q_{R}) + ℏ^{2} (R_{2} (A, P_{R}) + R_{1} (A, Q_{R})) + ℏ^{3} R_{2} (A, Q_{R}) .$
unlabeled · line 1278
$P_{L} = A W, Q_{L} = Q_{f, g}, P_{R} = W C, Q_{R} = Q^{R}_{g, f^{'}} .$

F7: four-order coherence, conditional on the missing maps

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