Manuscript X-A@1 · X-A.tex · definition · dc7f5c0a

Definition: Edge-regulated auxiliary density and coordinate operator

Regulator preflight › The regulated coordinate problem · lines 839–850

X-A@1#def:Aeps, X-A@1#eq:Aeps

For the formal metric $q = η + κh + κ^{2} k$ , set

A_{ε} [q]^{α β} = η^{α β} + σ_{ε} (A_{q}^{α β} - η^{α β}), D_{ε} [q] ψ = \partial_{α} (A_{ε} [q]^{α β} \partial_{β} ψ) .

The output of $D_{ε} [q]$ is a scalar density relative to $d^{4} x$ .

Displayed formulas in this passage

X-A@1#eq:Aeps · line 842
$A_{ε} [q]^{α β} = η^{α β} + σ_{ε} (A_{q}^{α β} - η^{α β}), D_{ε} [q] ψ = \partial_{α} (A_{ε} [q]^{α β} \partial_{β} ψ) .$