A scalar model of the coordinate contraction

The coordinate part of the bare insertion contains a derivative of ${{\mathsf{E}}_0}^{\mathrm{R}}(x,z)$. Consequently a representative time-ordered scalar contraction has the underlying product

The actual insertion has derivatives, tensor contractions, and smooth coefficient functions. Equation (eq:triangle) is used only to audit the scalar product criterion, not to assert the full loop coefficient equals this one term.

Choose the Hadamard orientation so that the first-slot Feynman covector is future-pointing at the later endpoint and past-pointing at the earlier endpoint. Reversing the Fourier convention reverses all these signs without changing the argument.

Define

It includes the corresponding partial coincidences and the total diagonal.