Manuscript XIX-B@1 · XIX-B.tex · section · b5670709

Lemma A: the density identity and the XIX-A comparison

Lemma A: the density identity and the XIX-A comparison · lines 291–307

XIX-B@1#eq:density-identity

For a formal metric $q$ with invertible zeroth-order coefficient, write

ρ_{q} = - det q, a_{q}^{α β} = ρ_{q} q^{α β} .

For a scalar $u$ , the scalar-wave definition gives

□_{q} u = ρ_{q}^{- 1} \partial_{α} (a_{q}^{α β} \partial_{β} u) .

Displayed formulas in this passage

XIX-B@1#eq:density-identity · line 301
$□_{q} u = ρ_{q}^{- 1} \partial_{α} (a_{q}^{α β} \partial_{β} u) .$
unlabeled · line 296
$ρ_{q} = - det q, a_{q}^{α β} = ρ_{q} q^{α β} .$