Manuscript X-L-ST@1 · X-L-ST.tex · section · 20a32a22

Two residuals with different types

Master residuals, reciprocity, and finite certificates › Two residuals with different types · lines 1320–1334

X-L-ST@1#eq:reciprocity

The classical master residual satisfies

∣ R_{cl} ∣ = 1, gh (R_{cl}) = 1.

By contrast, a reciprocity defect for an even classical source or response map $J$ , on even variations, has form

R_{rec} (r; u, v) = ⟨ u, D J (r) v ⟩ - ⟨ v, D J (r) u ⟩,

and is even with ghost number zero.

Displayed formulas in this passage

X-L-ST@1#eq:reciprocity · line 1328
$R_{rec} (r; u, v) = ⟨ u, D J (r) v ⟩ - ⟨ v, D J (r) u ⟩,$
unlabeled · line 1323
$∣ R_{cl} ∣ = 1, gh (R_{cl}) = 1.$