Manuscript X-A-ST@1 · X-A-ST.tex · section · d9ccbde1

Coordinate equations, with every ramp term

Flat Cauchy construction and coefficient equations › Coordinate equations, with every ramp term · lines 736–754

X-A-ST@1#eq:coordinateoperators

Set $B^{μν} = a_{1}^{μν} [k] + a_{2}^{μν} [h]$ . Then

D_{ε} [q] = □ + κ V_{ε} [h] + κ^{2} W_{ε} [h, k],

where

V_{ε} [h] ψ W_{ε} [h, k] ψ = σ \partial_{α} (a_{1}^{α β} [h] \partial_{β} ψ) + σ^{'} a_{1}^{0 β} [h] \partial_{β} ψ, = σ \partial_{α} (B^{α β} \partial_{β} ψ) + σ^{'} B^{0 β} \partial_{β} ψ .

Displayed formulas in this passage

X-A-ST@1#eq:coordinateoperators · line 745
$V_{ε} [h] ψ W_{ε} [h, k] ψ = σ \partial_{α} (a_{1}^{α β} [h] \partial_{β} ψ) + σ^{'} a_{1}^{0 β} [h] \partial_{β} ψ, = σ \partial_{α} (B^{α β} \partial_{β} ψ) + σ^{'} B^{0 β} \partial_{β} ψ .$
unlabeled · line 740
$D_{ε} [q] = □ + κ V_{ε} [h] + κ^{2} W_{ε} [h, k],$