Manuscript Hawk04-B@2 · Hawk04-B.tex · section · ba3b0713

The covariance convention

Additional channel debugging checks › The covariance convention · lines 2533–2552

With conjugate-linear annihilation,

e^{i t H_{B}} Φ (f) e^{- i t H_{B}} = Φ (e^{i t h_{B}} f),

and

⟨ Ω, Φ (e^{i s h_{B}} f_{a}) Φ (e^{i u h_{B}} f_{b}) Ω ⟩ = δ_{ab} \int_{μ}^{Λ} \frac{e ^{- i ω (s - u)}}{2 ω} d ω .

The Weyl amplitudes in Section sec:control use this convention. A prescribed scalar history is a comparison input, not a replacement for the complete matrix-unit channel of a noncommuting source.

Displayed formulas in this passage

unlabeled · line 2536
$e^{i t H_{B}} Φ (f) e^{- i t H_{B}} = Φ (e^{i t h_{B}} f),$
unlabeled · line 2541
$⟨ Ω, Φ (e^{i s h_{B}} f_{a}) Φ (e^{i u h_{B}} f_{b}) Ω ⟩ = δ_{ab} \int_{μ}^{Λ} \frac{e ^{- i ω (s - u)}}{2 ω} d ω .$