Manuscript XX-D@1 · XX-D.tex · section · c83a526d
Complete domain ledger
Regularized Wick substitution and operation ledger › Complete domain ledger · lines 1770–1925
| Operation | Sufficient condition or construction | Status here |
|---|---|---|
| Operation | Sufficient condition or construction | Status here |
| Classical local products in | Smooth spatial Schwartz coefficients; ordinary differentiation and multiplication | Defined on |
| Distributional local products | No opposite covectors at the same base point under D1 | Defined only when D1 holds; otherwise no raw product is assigned |
| Local free quadratic fields | Compact microcausal kernel and declared Wick subtraction; smooth diagonal remainder | Defined in the compact free Wick realization |
| First original rod | Compact or spatial Schwartz ; decaying Newton solution | Native classical map defined |
| Second original rod | Schwartz and | Defined classically; absent from |
| Fixed classical coordinate pullback | Diffeomorphism, or D2 for a more general map | Defined on its stated classical domain |
| Field-dependent quantum pullback | Each Taylor-product coefficient must already be admitted | Only its displayed retained jet is represented; no exact operator substitution |
| Equal-time restriction of | Null wavefront avoids the purely temporal conormal of the restriction map | Defined as a spatial distribution, not a smooth diagonal value |
| Raw diagonal contraction of | Ordinary diagonal pullback fails; use subtraction or a separately specified extension | No unrenormalized value assigned |
| Internal rod contraction near coincidence | Smooth equal-time times locally integrable , or Proposition prop:Taylor | Subtracted local operation constructed |
| Internal rod contraction at infinity | Assumption ass:internal | Conditional for the native representative |
| Compact-source Green response with one rod | Causal support and Lemma lem:Newton | Defined, with inverse-square tail |
| Native insertion times a compact regular probe, through one contraction | Assumptions ass:internal and ass:external | Theorem thm:native; hypotheses unverified for a selected representative |
| Two native lapse insertions through one contraction | Continuous covariance on the required two-endpoint noncompact test domain | Undefined here outside a separately verified domain |
| Two-rod covariance separation | Must preserve the canonical inverse-distance term | Universal inverse-square bound excluded |
| Time-ordered products against compact regular probes | Use the already normalized Feynman inverse as the single contraction, with its own noncompact estimates if needed | Compact single-line operation available; native infrared extension not inferred |
| Products of several propagator distributions, higher Wick contractions, or interacting graphs | Joint wavefront, extension, and infrared analysis for the actual graph | Not constructed by the one-contraction theorem |