Manuscript X-A-conv@1 · X-A-conv.tex · section · c76fffa3

The defects at both retained infinitesimal orders

Relational expansion and retained infinitesimal defects › The defects at both retained infinitesimal orders · lines 1258–1286

X-A-conv@1#eq:Rtwo

For the bare functional $k = 0$ , split

δ_{ξ} = δ_{ξ}^{(0)} + κ δ_{ξ}^{(1)},

where

δ_{ξ}^{(0)} h = K ξ, δ_{ξ}^{(0)} ϕ = 0, δ_{ξ}^{(1)} h = L_{ξ} h, δ_{ξ}^{(1)} ϕ = X_{ξ} ϕ .

Put

a = S_{ε} ξ, d_{2} = E_{0} C T_{g, ε} (L_{ξ} h) + 2 V (H, K a),

and

R_{2, ξ} = d_{2} - X_{ξ} w,

where $X_{ξ} w$ means the vector with components $ξ^{ν} \partial_{ν} w^{μ}$ .

Displayed formulas in this passage

X-A-conv@1#eq:Rtwo · line 1278
$R_{2, ξ} = d_{2} - X_{ξ} w,$
unlabeled · line 1261
$δ_{ξ} = δ_{ξ}^{(0)} + κ δ_{ξ}^{(1)},$
unlabeled · line 1265
$δ_{ξ}^{(0)} h = K ξ, δ_{ξ}^{(0)} ϕ = 0, δ_{ξ}^{(1)} h = L_{ξ} h, δ_{ξ}^{(1)} ϕ = X_{ξ} ϕ .$
unlabeled · line 1272
$a = S_{ε} ξ, d_{2} = E_{0} C T_{g, ε} (L_{ξ} h) + 2 V (H, K a),$