Manuscript VII-A-ST@1 · VII-A-ST.tex · section · c39a67a3

Unswitched harmonic labels and the relational coefficients

Unswitched harmonic labels and the relational coefficients · lines 631–653

Define

C^{μ} [h] = \partial_{ν} h^{ν μ} - \frac{1}{2} \partial^{μ} tr_{η} h = - \partial_{ν} A^{ν μ} (h) .

The harmonic labels are four scalar functions

X_{γ}^{μ} = x^{μ} + κ w^{μ} + κ^{2} v^{μ} (mod κ^{3})

satisfying the unswitched equation

\partial_{α} (A_{γ}^{α β} \partial_{β} X_{γ}^{μ}) = 0 (mod κ^{3})

and data $X_{γ}^{μ} ∣_{0} = x^{μ} ∣_{0}$ , $\partial_{t} X_{γ}^{μ} ∣_{0} = \partial_{t} x^{μ} ∣_{0}$ .

Displayed formulas in this passage

unlabeled · line 635
$C^{μ} [h] = \partial_{ν} h^{ν μ} - \frac{1}{2} \partial^{μ} tr_{η} h = - \partial_{ν} A^{ν μ} (h) .$
unlabeled · line 642
$X_{γ}^{μ} = x^{μ} + κ w^{μ} + κ^{2} v^{μ} (mod κ^{3})$
unlabeled · line 646
$\partial_{α} (A_{γ}^{α β} \partial_{β} X_{γ}^{μ}) = 0 (mod κ^{3})$