Manuscript VII-I@1 · VII-I.tex · section · 907e96ab

A positive scalar diagnostic with a fixed classical metric

Interactions, normalization, and a controlled diagnostic › A positive scalar diagnostic with a fixed classical metric · lines 2014–2031

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Fix a smooth classical metric jet $(h, k)$ , a finite width, and retain only the scalar as a quantum field. The prepared relational coefficient is scalar-linear, so there is a compact smooth test

d_{κ} = f + κ d_{1} + κ^{2} d_{2}

such that

O_{f, ϵ}^{D} [h, k, ϕ] = ϕ (d_{κ}) (mod κ^{3}) .

Smoothness follows either by transposition through the smooth classical coefficients or by the one-external-slot case of Lemma lem:tree.

Displayed formulas in this passage

unlabeled · line 2020
$d_{κ} = f + κ d_{1} + κ^{2} d_{2}$
unlabeled · line 2024
$O_{f, ϵ}^{D} [h, k, ϕ] = ϕ (d_{κ}) (mod κ^{3}) .$

Nearby in this section

proposition: Proposition: Positive marginal state evaluation
section: A positive scalar diagnostic with a fixed classical metric