Manuscript XX-E@1 · XX-E.tex · section · cf7a8f40

The operation that can be constructed independently

Explicit Newton-contact images and comparison Ward images › The operation that can be constructed independently · lines 918–942

XX-E@1#eq:sourcecontact

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For a finite spatial multiindex family, consider the vector-valued source kernel

b^{ia} (t, y; t^{'}, z) = δ (t - t^{'}) ∣ α ∣ \leq m \sum c_{α}^{ia} (t, y, z) \partial_{y}^{α} δ^{3} (y - z),

where the coefficients are smooth and compactly supported in the tangential variables used below. This is an explicit contact family, not a claimed exhaustive native quantum counterterm class.

Its rod image is

J^{a} = \int P_{i} (x - y) b^{ia} (t, y; t^{'}, z) d^{3} y .

Displayed formulas in this passage

XX-E@1#eq:sourcecontact · line 922
$b^{ia} (t, y; t^{'}, z) = δ (t - t^{'}) ∣ α ∣ \leq m \sum c_{α}^{ia} (t, y, z) \partial_{y}^{α} δ^{3} (y - z),$
unlabeled · line 937
$J^{a} = \int P_{i} (x - y) b^{ia} (t, y; t^{'}, z) d^{3} y .$

The operation that can be constructed independently

Displayed formulas in this passage

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