Manuscript XII-E@1 · XII-E.tex · definition · 9471ea56

Definition: The named coefficient

E1: the gravitational coefficient and the named functional · lines 634–649

XII-E@1#def:PhiD, XII-E@1#eq:PhiD

The metric-sourced second-order relational coefficient on the scalar-linear sector is

Φ^{(2)}_{D} (f, g) [γ, ϕ] := A_{2}^{sc} [f, g] (γ, r_{D} [γ]; ϕ), r_{D} [γ] = - u_{D} [γ] .

It is cubic in $γ$ -and- $ϕ$ jointly, of degree $(2, 1)$ , with the scalar slot $ϕ$ ranging over all smooth configurations. The scalar-sourced slot $r_{g} [ϕ]$ is treated separately in Corollary cor:scalarsourced.

Displayed formulas in this passage

XII-E@1#eq:PhiD · line 638
$Φ^{(2)}_{D} (f, g) [γ, ϕ] := A_{2}^{sc} [f, g] (γ, r_{D} [γ]; ϕ), r_{D} [γ] = - u_{D} [γ] .$

Nearby in this section

remark: Remark: One metric field
proposition: Proposition: The gauge-fixed second metric coefficient
section: E1: the gravitational coefficient and the named functional
proposition: Proposition: Single entry, with its sign
remark: Remark: Correction to the brief