Manuscript VI@1 · VI.tex · section · b5b60afb

Explicit scalar operator expansion

Finite-time harmonic coordinates and second-order descent › Explicit scalar operator expansion · lines 840–852

VI@1#eq:C-h

For $h$ , define

d_{h} e_{h} A_{h}^{μν} C_{h}^{μν} = \frac{1}{2} tr_{η} h, = \frac{1}{8} (tr_{η} h)^{2} - \frac{1}{4} h_{α β} h^{α β}, = d_{h} η^{μν} - h^{μν}, = h^{μ}_{ρ} h^{ρ ν} - d_{h} h^{μν} + e_{h} η^{μν} .

Displayed formulas in this passage

VI@1#eq:C-h · line 843
$d_{h} e_{h} A_{h}^{μν} C_{h}^{μν} = \frac{1}{2} tr_{η} h, = \frac{1}{8} (tr_{η} h)^{2} - \frac{1}{4} h_{α β} h^{α β}, = d_{h} η^{μν} - h^{μν}, = h^{μ}_{ρ} h^{ρ ν} - d_{h} h^{μν} + e_{h} η^{μν} .$