Manuscript IX-D@3 · IX-D-v3.tex · section · 3ad4586e

Subtraction and the smooth sign comparison

D1: domains and separate causal interfaces › Subtraction and the smooth sign comparison · lines 923–941

IX-D@3#eq:subtraction

On a domain where both maps exist, a proposed unnormalized comparison is

R (V; O) = i (T_{2} (V, O) - V ⋆_{c} O) .

It is not yet a definition in this manuscript, since $T_{2}$ has not been constructed. The conditional theorem in Section sec:D5 states precisely when this comparison has the desired properties.

Replacing $V ⋆_{c} O$ by $V O$ is a different prescription. It requires a separate identity eliminating the relevant free contractions. A specialized comparison reported for another sector does not supply that identity here.

Displayed formulas in this passage

IX-D@3#eq:subtraction · line 927
$R (V; O) = i (T_{2} (V, O) - V ⋆_{c} O) .$

Nearby in this section

assumption: Assumption: Smooth Duhamel comparison
lemma: Lemma: Smooth comparison sign
section: Subtraction and the smooth sign comparison
theorem: Theorem: D1: causal structure remains additional