Manuscript Em01-F@3 · Em01-F-v3.tex · section · 225e59af

Crossed-line reduction on the actual time-ordering region

Exact localized crossed-line and tensor regrouping › Crossed-line reduction on the actual time-ordering region · lines 2703–2719

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The scalar profile (eq:dprofile) is still an eight-dimensional convolution:

d_{δ} (x_{1}, x_{2}) = ⟨ ζ χ (W_{0} \otimes Δ_{m}), δ^{- 8} ρ ((x_{1} - v_{1}) / δ, (x_{2} - v_{2}) / δ) ⟩ .

A general $ρ (H_{1}, H_{2})$ need not factor. No replacement by two independently chosen four-dimensional mollifiers is made.

The lemma is an exact positive-scale localization identity. It does not authorize multiplying $W_{0} \otimes Δ_{m}$ by an internal singular kernel at $δ = 0$ .

Displayed formulas in this passage

unlabeled · line 2707
$d_{δ} (x_{1}, x_{2}) = ⟨ ζ χ (W_{0} \otimes Δ_{m}), δ^{- 8} ρ ((x_{1} - v_{1}) / δ, (x_{2} - v_{2}) / δ) ⟩ .$

Nearby in this section

section: Crossed-line reduction on the actual time-ordering region
lemma: Lemma: Localized scalar crossed distribution