Manuscript XIX-D@1 · XIX-D.tex · section · 1f47e33b

Pure-trace tests have an explicit blind sector

Witness data do not determine kernels or admission › Pure-trace tests have an explicit blind sector · lines 557–572

Use the flat signature $η = diag (1, - 1, - 1, - 1)$ for this subsection. A compact three-slot kernel has two symmetric tensor slots and one scalar slot:

K^{μν, ρ σ} (x_{1}, x_{2}, x_{3}) .

Its pure-trace evaluation is its pairing with

(η_{μν} ψ_{1} (x_{1})) \otimes (η_{ρ σ} ψ_{2} (x_{2})) \otimes ϕ (x_{3}) .

Displayed formulas in this passage

unlabeled · line 563
$K^{μν, ρ σ} (x_{1}, x_{2}, x_{3}) .$
unlabeled · line 567
$(η_{μν} ψ_{1} (x_{1})) \otimes (η_{ρ σ} ψ_{2} (x_{2})) \otimes ϕ (x_{3}) .$

Nearby in this section

proposition: Proposition: Pure-trace data do not determine the smooth kernel or its free-shell functional
section: Pure-trace tests have an explicit blind sector