Manuscript XIV-H@1 · XIV-H.tex · section · 695c7c3a

The noncharacteristic internal diagonal

H2d: the two internal placements in K 5 › The noncharacteristic internal diagonal · lines 1365–1395

XIV-H@1#eq:Ldiag

Consider the first placement near $a = z$ , with $b - a$ a nonzero future null separation. In the relative internal variable $r = a - z$ , the retarded kernel has a diagonal operator part. Away from the internal characteristic covectors

p (κ) = η^{μν} κ_{μ} κ_{ν} = 0,

its leading Fourier multiplier is $- 1/ p (κ)$ , because the symbol of $□$ is $- p (κ)$ .

This describes the ordinary elliptic diagonal chart of the fixed retarded kernel. It is not an ellipticity assertion on its characteristic set.

The corresponding diagonal kernel relation is

Λ_{d, +} = {(w, θ d ((b - a)^{2}) + κ_{μ} d (a^{μ} - z^{μ})) : (b - a)^{2} = 0, a = z} ∖ 0.

The second placement has the analogous formula with $b - z$ and $z - a$ .

Displayed formulas in this passage

XIV-H@1#eq:Ldiag · line 1383
$Λ_{d, +} = {(w, θ d ((b - a)^{2}) + κ_{μ} d (a^{μ} - z^{μ})) : (b - a)^{2} = 0, a = z} ∖ 0.$
unlabeled · line 1372
$p (κ) = η^{μν} κ_{μ} κ_{ν} = 0,$

The noncharacteristic internal diagonal

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