Manuscript Em01-F@3 · Em01-F-v3.tex · section · 225e59af

The grouped array

Four contraction kernels in the actual relative slots › The grouped array · lines 1743–1769

Em01-F@3#eq:actualC

The actual crossed distribution is

C_{I}^{μν} (x_{1}, x_{2}) = ℏ^{2} N^{μν}_{I} [D_{T, 0} (x_{1}) \otimes D_{T, m} (x_{2}) - W_{0} (x_{1}) \otimes W_{m} (x_{2})] .

Its factors are in independent variables. The linear map

f (a, b, z, y) = (y - a, y - b)

is a submersion, so the pullback of this array exists. This does not define its singular product with $K_{ret}$ .

The role of a contraction prescription, and the additional extension issue for time-ordered products, are distinct even when their formal kernel expressions are available FR (Sections 5–7).

Displayed formulas in this passage

Em01-F@3#eq:actualC · line 1746
$C_{I}^{μν} (x_{1}, x_{2}) = ℏ^{2} N^{μν}_{I} [D_{T, 0} (x_{1}) \otimes D_{T, m} (x_{2}) - W_{0} (x_{1}) \otimes W_{m} (x_{2})] .$
unlabeled · line 1758
$f (a, b, z, y) = (y - a, y - b)$