Manuscript V@1 · V.tex · figure · e7ddf37d

Subcritical extension

The external-metric first retarded product › Scaling degree and unique minimal extension · lines 2192–2220

V@1#fig:subcritical-extension

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metricscalarrepresented quantumdefect / unresolvedsupport / scope
2W, W^F≤ 3∂Wthreshold 4δ and ∂δ sit at ≥ 4
No nonzero origin-supported difference preserves the coefficientwise actual scaling degree.
PWmF=iδPW_m^{\mathrm F}=i\delta is a fixed differentiated field-equation contact, not an independent extension parameter.
This insertion pair only. Fixed mass. Specified coefficientwise normalization. No conclusion for T2(V,V)T_2(V,V).

Subcritical extension for the specified insertion pair. Numerical coefficients have relative scaling degree at most three in four dimensions, whereas every nonzero origin-supported counterterm has degree at least four. Thus the stated minimal normalization has no independent diagonal parameter. Differentiated field-equation contacts are fixed by the normalized contractions BF.

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