Manuscript VII-I@1 · VII-I.tex · section · 907e96ab

Classical equivalence, not an independent coordinate field

Route B3: constrained auxiliary coordinates › Classical equivalence, not an independent coordinate field · lines 1550–1562

VII-I@1#eq:auxiliary-constraints

Introduce auxiliary smooth variables $w^{μ}, v^{μ}$ , and impose

□ w^{μ} □ v^{μ} w ∣_{Σ} = \partial_{t} w ∣_{Σ} = C^{μ} h, = C^{μ} k - \partial_{α} a_{2}^{α μ} [h] - \partial_{α} (a_{1}^{α β} [h] \partial_{β} w^{μ}), = v ∣_{Σ} = \partial_{t} v ∣_{Σ} = 0.

Displayed formulas in this passage

VII-I@1#eq:auxiliary-constraints · line 1553
$□ w^{μ} □ v^{μ} w ∣_{Σ} = \partial_{t} w ∣_{Σ} = C^{μ} h, = C^{μ} k - \partial_{α} a_{2}^{α μ} [h] - \partial_{α} (a_{1}^{α β} [h] \partial_{β} w^{μ}), = v ∣_{Σ} = \partial_{t} v ∣_{Σ} = 0.$