Manuscript VII-D@1 · VII-D.tex · section · ef67c89c

Normalization ledger

The reflected radial family: normalization and Lemma A › Normalization ledger · lines 1006–1025

VII-D@1#eq:Adef

As a consequence of the ledger, the intrinsic definition (eq:Aintrinsic) can now be written

⟨ A (r), Φ ⟩ = c_{0} r^{3} ω (r) \int_{S^{2}} d Ω (ν) \int d t d s d t^{'} d^{3} y \times \int \frac{d ^{3} α d ^{3} β}{( 2 π ) ^{6} P ^{2} P ^{'2}} e^{i [(P - ω (r)) t - (P^{'} - ω (r)) t^{'} + (P - P^{'}) s]} H_{Φ} (t, s, t^{'}, y; α, β) .

The formula for $A_{ε}^{ρ} (r)$ has the two additional factors $ϑ (εP) ϑ (ε P^{'})$ .

Displayed formulas in this passage

VII-D@1#eq:Adef · line 1010
$⟨ A (r), Φ ⟩ = c_{0} r^{3} ω (r) \int_{S^{2}} d Ω (ν) \int d t d s d t^{'} d^{3} y \times \int \frac{d ^{3} α d ^{3} β}{( 2 π ) ^{6} P ^{2} P ^{'2}} e^{i [(P - ω (r)) t - (P^{'} - ω (r)) t^{'} + (P - P^{'}) s]} H_{Φ} (t, s, t^{'}, y; α, β) .$