Manuscript Em06-A@1 · Em06-A-v1.tex · definition · ee9923c6

Definition: The named observable

The classical object before the limit › Green operators and the harmonic coordinate coefficient · lines 293–310

Em06-A@1#def:observable, Em06-A@1#eq:observable

The observable of Em06-A is exactly

O_{f} [h; ϕ_{0}] = \int_{M} f (x) (ϕ_{1, χ} [h; ϕ_{0}] (x) - w [h]^{μ} (x) \partial_{μ} ϕ_{0} (x)) d^{4} x .

It is the first coefficient of the relational scalar obtained by composing the switched scalar solution with the inverse harmonic coordinate map and integrating against the fixed density in relational-coordinate space.

Displayed formulas in this passage

Em06-A@1#eq:observable · line 296
$O_{f} [h; ϕ_{0}] = \int_{M} f (x) (ϕ_{1, χ} [h; ϕ_{0}] (x) - w [h]^{μ} (x) \partial_{μ} ϕ_{0} (x)) d^{4} x .$

Nearby in this section

section: Green operators and the harmonic coordinate coefficient
section: Green operators and the harmonic coordinate coefficient
remark: Remark: What the background notation means