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

Reversed and conjugate comparison domains

D1: domains and separate causal interfaces › Reversed and conjugate comparison domains · lines 783–804

IX-D@3#eq:freeinvolution, IX-D@3#eq:Dcmp

On the ambient tensor space define

σ (F \otimes G) = G \otimes F, γ (F \otimes G) = F^{*} \otimes G^{*}, d^{†} = σ γ d .

The inherited domain is dagger stable, and

(F ⋆_{c} G)^{*} = G^{*} ⋆_{c} F^{*}

where the pair is declared.

Dagger stability alone does not assert separate flip stability. To use both free orderings without an enlargement, define

D_{cmp} = D_{decl} \cap σ (D_{decl}) .

Displayed formulas in this passage

IX-D@3#eq:freeinvolution · line 792
$(F ⋆_{c} G)^{*} = G^{*} ⋆_{c} F^{*}$
IX-D@3#eq:Dcmp · line 800
$D_{cmp} = D_{decl} \cap σ (D_{decl}) .$
unlabeled · line 786
$σ (F \otimes G) = G \otimes F, γ (F \otimes G) = F^{*} \otimes G^{*}, d^{†} = σ γ d .$