Manuscript IX-E-2@1 · IX-E-2.tex · section · e70d9077

Exact direct-plus-reflected subtraction

Exact direct-plus-reflected subtraction · lines 600–616

IX-E-2@1#eq:D-fourier, IX-E-2@1#eq:H-fourier

Define the Fourier distributions

D (v, z) H (v, z) = \int_{R^{3}} \frac{d ^{3} p}{( 2 π ) ^{3}} e^{i p \cdot z} \frac{sin ( ∣ p ∣ v )}{∣ p ∣}, = \int_{R^{3}} \frac{d ^{3} p}{( 2 π ) ^{3}} e^{i p \cdot z} \frac{cos ( ∣ p ∣ v )}{∣ p ∣ ^{2}} .

The same argument as above defines these distributions and their Abel-regulated versions. The letter $H$ here denotes only this cosine distribution; it is not a new Wick covariance.

Displayed formulas in this passage

IX-E-2@1#eq:D-fourier · line 603
$D (v, z) H (v, z) = \int_{R^{3}} \frac{d ^{3} p}{( 2 π ) ^{3}} e^{i p \cdot z} \frac{sin ( ∣ p ∣ v )}{∣ p ∣}, = \int_{R^{3}} \frac{d ^{3} p}{( 2 π ) ^{3}} e^{i p \cdot z} \frac{cos ( ∣ p ∣ v )}{∣ p ∣ ^{2}} .$
IX-E-2@1#eq:H-fourier · line 603
$D (v, z) H (v, z) = \int_{R^{3}} \frac{d ^{3} p}{( 2 π ) ^{3}} e^{i p \cdot z} \frac{sin ( ∣ p ∣ v )}{∣ p ∣}, = \int_{R^{3}} \frac{d ^{3} p}{( 2 π ) ^{3}} e^{i p \cdot z} \frac{cos ( ∣ p ∣ v )}{∣ p ∣ ^{2}} .$

Exact direct-plus-reflected subtraction

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