Manuscript IX-E@1 · IX-E.tex · section · 8f8d5e7f

Conjugation conventions

Prerequisites and entering state › Conjugation conventions · lines 362–387

IX-E@1#eq:free-star

Let $σ (F \otimes G) = G \otimes F$ be complex-linear flip. Let

γ (F \otimes G) = F^{*} \otimes G^{*}

be componentwise antilinear conjugation. Then

d^{†} = σ γ d, σ^{2} = γ^{2} = id, σ γ = γ σ .

Conjugation fixes the formal parameter $ℏ$ . The inherited reversal property is

D_{decl}^{†} = D_{decl}, ⋆_{c} (d)^{*} = ⋆_{c} (d^{†}) .

The comparison domain is

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

Thus both free orderings exist on $D_{cmp}$ . Flip stability of all of $D_{decl}$ is not assumed.

Displayed formulas in this passage

IX-E@1#eq:free-star · line 375
$D_{decl}^{†} = D_{decl}, ⋆_{c} (d)^{*} = ⋆_{c} (d^{†}) .$
unlabeled · line 365
$γ (F \otimes G) = F^{*} \otimes G^{*}$
unlabeled · line 369
$d^{†} = σ γ d, σ^{2} = γ^{2} = id, σ γ = γ σ .$
unlabeled · line 382
$D_{cmp} = D_{decl} \cap σ (D_{decl}) .$