Manuscript IV@1 · IV.tex · section · 351cb2d7

Scalar identification and formal coefficients

Model 1: the fixed vacuum TT plane › Scalar identification and formal coefficients · lines 887–913

IV@1#eq:Fplane

For completeness, the admitted first-order family consists of

(h, ϕ_{0}, ϕ_{1}) = (k + K ξ, ϕ_{0}, S_{t_{0}} (k) ϕ_{0} + X_{ξ} ϕ_{0}) .

The complete coefficient expression

\int f [ϕ_{0} + κ (ϕ_{1} - X_{w (h)} ϕ_{0})] d^{4} x, κ^{2} = 0,

is unchanged by adding a compact gauge parameter, since both $w (h)$ and $ϕ_{1}$ change by that parameter's prescribed action. On the selected section it is

F_{f}^{[1]} = ℓ_{0, f} + κ (q ℓ_{e, f} + π ℓ_{r, f}), ℓ_{0, f} = \int f ϕ_{0}, ℓ_{a, f} = \int f S_{t_{0}} (a) ϕ_{0} .

No sourced second metric coefficient occurs here.

Displayed formulas in this passage

IV@1#eq:Fplane · line 904
$F_{f}^{[1]} = ℓ_{0, f} + κ (q ℓ_{e, f} + π ℓ_{r, f}), ℓ_{0, f} = \int f ϕ_{0}, ℓ_{a, f} = \int f S_{t_{0}} (a) ϕ_{0} .$
unlabeled · line 890
$(h, ϕ_{0}, ϕ_{1}) = (k + K ξ, ϕ_{0}, S_{t_{0}} (k) ϕ_{0} + X_{ξ} ϕ_{0}) .$
unlabeled · line 896
$\int f [ϕ_{0} + κ (ϕ_{1} - X_{w (h)} ϕ_{0})] d^{4} x, κ^{2} = 0,$

Scalar identification and formal coefficients

Displayed formulas in this passage

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