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

Metric jet and density coefficients

Convention sheet › Metric jet and density coefficients · lines 583–595

X-A@1#eq:C

Two identities used repeatedly follow from (eq:a):

C^{μ} [h] := \partial_{ν} h^{ν μ} - \frac{1}{2} \partial^{μ} h = - \partial_{ν} a_{1}^{ν μ} [h], C^{μ} [K ξ] = □ ξ^{μ} .

For the second, $tr K ξ = 2 \partial_{ρ} ξ^{ρ}$ and $\partial_{ν} (K ξ)^{ν μ} = □ ξ^{μ} + \partial^{μ} \partial_{ρ} ξ^{ρ}$ .

Displayed formulas in this passage

X-A@1#eq:C · line 586
$C^{μ} [h] := \partial_{ν} h^{ν μ} - \frac{1}{2} \partial^{μ} h = - \partial_{ν} a_{1}^{ν μ} [h], C^{μ} [K ξ] = □ ξ^{μ} .$