Manuscript Em02-D@4 · Em02-D-v4.tex · section · fcf2fac7

Retarded cone measure

Fixed model, root, and localization › Retarded cone measure · lines 246–269

Em02-D@4#eq:R, Em02-D@4#eq:B

Define

⟨ R, ψ ⟩ = \frac{1}{4 π} \int_{0}^{\infty} β \int_{S^{2}} ψ (β, β n) d n d β .

Sphere area measure has total mass $4 π$ . Away from the vertex,

R (x) = \frac{δ ( x ^{0} - ∣ x ∣ )}{4 π ∣ x ∣} .

Set

B (x) = \frac{1}{8 π} Θ (x^{0} - ∣ x ∣) .

The identity $R * R = B$ will be proved below.

Displayed formulas in this passage

Em02-D@4#eq:R · line 249
$⟨ R, ψ ⟩ = \frac{1}{4 π} \int_{0}^{\infty} β \int_{S^{2}} ψ (β, β n) d n d β .$
Em02-D@4#eq:B · line 264
$B (x) = \frac{1}{8 π} Θ (x^{0} - ∣ x ∣) .$
unlabeled · line 259
$R (x) = \frac{δ ( x ^{0} - ∣ x ∣ )}{4 π ∣ x ∣} .$