Manuscript Oai282-B@1 · Oai282-B.tex · definition · f2956de5

Definition: Elementary retarded current insertion

The explicit current contact calculation › Retarded elementary insertion · lines 902–924

Oai282-B@1#def:C, Oai282-B@1#eq:Cexplicit

Let $C_{X}^{μ} (x, y)$ be the polarization of $j_{X}^{μ} (x)$ obtained by replacing one elementary scalar factor by $R (x - y)$ :

C_{X}^{μ} (x, y) = X_{ν} (x) [\partial^{μ} ϕ (x) \partial^{ν} R (x - y) + \partial^{μ} R (x - y) \partial^{ν} ϕ (x) - η^{μν} \partial_{ρ} ϕ (x) \partial^{ρ} R (x - y) + \frac{1}{3} (η^{μν} □_{x} - \partial_{x}^{μ} \partial_{x}^{ν}) (ϕ (x) R (x - y))] .

It is understood as a weak field distribution on $D_{E} \times D_{E}$ .

Displayed formulas in this passage

Oai282-B@1#eq:Cexplicit · line 906
$C_{X}^{μ} (x, y) = X_{ν} (x) [\partial^{μ} ϕ (x) \partial^{ν} R (x - y) + \partial^{μ} R (x - y) \partial^{ν} ϕ (x) - η^{μν} \partial_{ρ} ϕ (x) \partial^{ρ} R (x - y) + \frac{1}{3} (η^{μν} □_{x} - \partial_{x}^{μ} \partial_{x}^{ν}) (ϕ (x) R (x - y))] .$