Manuscript IV@1 · IV.tex · section · 351cb2d7

Normal-ordered source and the reconstructed form

Model 3: scalar stress form and exterior record › Normal-ordered source and the reconstructed form · lines 2602–2627

IV@1#eq:Wick3

There is only scalar Fock space:

H_{3} = Γ_{s} (h_{ϕ}), h_{ϕ} = L^{2} (R^{3}, d p) .

Put

ω_{p} = ∣ p ∣^{2} + m^{2}, n_{p} = (2 π)^{- 3/2} (2 ω_{p})^{- 1/2}, u_{p} (t, x) = n_{p} e^{- i ω_{p} t + i p \cdot x} .

Let $D_{3} = Γ_{s}^{alg} (S (R^{3}))$ , and use the minimal vacuum-normal-ordered stress

: T_{μν} :=: \partial_{μ} ϕ \partial_{ν} ϕ : - \frac{1}{2} η_{μν} : (\partial^{α} ϕ \partial_{α} ϕ + m^{2} ϕ^{2}) : .

This is a fixed prescription. No improvement or constant counterterm is left unspecified.

Displayed formulas in this passage

unlabeled · line 2605
$H_{3} = Γ_{s} (h_{ϕ}), h_{ϕ} = L^{2} (R^{3}, d p) .$
unlabeled · line 2610
$ω_{p} = ∣ p ∣^{2} + m^{2}, n_{p} = (2 π)^{- 3/2} (2 ω_{p})^{- 1/2}, u_{p} (t, x) = n_{p} e^{- i ω_{p} t + i p \cdot x} .$
IV@1#eq:Wick3 · line 2617
$: T_{μν} :=: \partial_{μ} ϕ \partial_{ν} ϕ : - \frac{1}{2} η_{μν} : (\partial^{α} ϕ \partial_{α} ϕ + m^{2} ϕ^{2}) : .$