Manuscript Em03-C@1 · Em03-C-v1.tex · assumption · 47dd71ec

Assumption: Stationary outgoing radiation input

C0: the complete two-packet semiclassical baseline › Inherited state and the covariance convention · lines 298–324

Em03-C@1#ass:radiation, Em03-C@1#eq:radiationdensity

Fix one real angular harmonic of degree $ℓ$ in the massless scalar model of Em03-A. The outgoing radiation state is centered, gauge-invariant, regular, and quasifree, with

⟨ a_{out} (ω)^{†} a_{out} (ω^{'})⟩ = n (ω) δ (ω - ω^{'}), ⟨ a_{out} (ω) a_{out} (ω^{'})⟩ = 0,

where

n (ω) = \frac{Γ _{ℓ} ( ω )}{e ^{β_{H} ω} - 1}, β_{H} = 8 π GM, 0 \leq Γ_{ℓ} (ω) \leq 1.

Annihilation tests are conjugate-linear:

a (h) = \int_{0}^{\infty} h (ω) a_{out} (ω) d ω .

Displayed formulas in this passage

Em03-C@1#eq:radiationdensity · line 311
$n (ω) = \frac{Γ _{ℓ} ( ω )}{e ^{β_{H} ω} - 1}, β_{H} = 8 π GM, 0 \leq Γ_{ℓ} (ω) \leq 1.$
unlabeled · line 303
$⟨ a_{out} (ω)^{†} a_{out} (ω^{'})⟩ = n (ω) δ (ω - ω^{'}), ⟨ a_{out} (ω) a_{out} (ω^{'})⟩ = 0,$
unlabeled · line 320
$a (h) = \int_{0}^{\infty} h (ω) a_{out} (ω) d ω .$

Assumption: Stationary outgoing radiation input

Displayed formulas in this passage

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