Manuscript XVI-J@1 · XVI-J.tex · proposition · 6c1f306d

Proposition: Propagated contact term

Propagated ambiguity and limits of the construction · lines 1449–1471 · proof included or linked

XVI-J@1#prop:ambiguity, XVI-J@1#eq:ambiguity

If the numerical extension changes by $cδ$ , then

Δ C_{2 e}^{R} (h, φ) = c ⟨ B_{f, g, μν} (y, x), χ_{I} (y) K^{μν} (y, y; h) φ (x) ⟩ .

In particular, the change of subtraction function is obtained by taking $c = T_{0} (ϖ_{1} - ϖ_{2})$ .

Proof. The product of the pulled-back root and $δ (y - w)$ satisfies the same noncancellation test as Theorem thm:attachment. Proper integration in $w$ evaluates the smooth coefficient on $w = y$ , leaving the distributional root pairing in (eq:ambiguity).

Displayed formulas in this passage

XVI-J@1#eq:ambiguity · line 1452
$Δ C_{2 e}^{R} (h, φ) = c ⟨ B_{f, g, μν} (y, x), χ_{I} (y) K^{μν} (y, y; h) φ (x) ⟩ .$

Nearby in this section

section: Propagated ambiguity and limits of the construction