Manuscript Hawk04-A@1 · Hawk04-A.tex · section · 526092ba

The Gaussian covariance sign convention

Additional debugging checks › The Gaussian covariance sign convention · lines 2193–2214

With annihilation conjugate-linear in $f$ ,

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

and

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

This covariance convention is consistent with the coherent amplitude used in Theorem thm:four-majorana. A prescribed scalar-history calculation does not replace the noncommuting source channel on all matrix units.

Displayed formulas in this passage

unlabeled · line 2196
$e^{i t H_{B}} Φ (f) e^{- i t H_{B}} = Φ (e^{i t h_{B}} f),$
unlabeled · line 2202
$⟨ Ω_{bath}, Φ (e^{i s h_{B}} f_{a}) Φ (e^{i u h_{B}} f_{b}) Ω_{bath} ⟩ = δ_{ab} \int_{μ}^{Λ} \frac{e ^{- i ω (s - u)}}{2 ω} d ω .$