The convention and its forced ordered values

We adopt

The zeroth-order term of ${{\mathsf{T}}_2}^{\mathrm{ren}}$ is the ordinary product ${\mathcal{V}}_g\mathcal{O}$. On regular kernels the even time-ordered line in this convention is

For the vertex variables $y$ and observable variables $x$, it equals $H(y,x)$ when the vertex is later and $H^{\mathsf{T}}(y,x)$ when the observable is later. This follows directly from $H-H^{\mathsf{T}}=i({G_{\mathrm{act}}}^{\mathrm{R}}-{G_{\mathrm{act}}}^{\mathrm{A}})$ and causal support.

The usual distinction between a time-ordered normalization and the corresponding retarded difference is made in the functional formulation of causal perturbation theory FR (Sections 6–7). Here the consequences are checked with the stated signs.