Manuscript XII-C@1 · XII-C.tex · section · dead1004

An explicit ramp defect with no third derivatives

C2: the changed fixed-background Noether identity › An explicit ramp defect with no third derivatives · lines 878–911

XII-C@1#eq:Rampdef, XII-C@1#eq:Rampdef-time

Define

R_{σ_{ε}, ν} = 2 η_{ρ ν} (\partial_{μ} σ_{ε}) J_{3}^{μ ρ} + 4 η_{ρ ν} [(\partial_{μ} C_{2}^{μ ρ α β}) \partial_{α} \partial_{β} σ_{ε} - (\partial_{μ} M_{2}^{μ ρ λ}) \partial_{λ} σ_{ε} - M_{2}^{μ ρ λ} \partial_{μ} \partial_{λ} σ_{ε}] .

For the declared ramp this is

R_{σ_{ε}, ν} = 2 η_{ρ ν} J_{3}^{0 ρ} σ_{ε}^{'} + 4 η_{ρ ν} [(\partial_{μ} C_{2}^{μ ρ 00}) σ_{ε}^{''} - (\partial_{μ} M_{2}^{μ ρ 0}) σ_{ε}^{'} - M_{2}^{0 ρ 0} σ_{ε}^{''}] .

Displayed formulas in this passage

XII-C@1#eq:Rampdef · line 881
$R_{σ_{ε}, ν} = 2 η_{ρ ν} (\partial_{μ} σ_{ε}) J_{3}^{μ ρ} + 4 η_{ρ ν} [(\partial_{μ} C_{2}^{μ ρ α β}) \partial_{α} \partial_{β} σ_{ε} - (\partial_{μ} M_{2}^{μ ρ λ}) \partial_{λ} σ_{ε} - M_{2}^{μ ρ λ} \partial_{μ} \partial_{λ} σ_{ε}] .$
XII-C@1#eq:Rampdef-time · line 898
$R_{σ_{ε}, ν} = 2 η_{ρ ν} J_{3}^{0 ρ} σ_{ε}^{'} + 4 η_{ρ ν} [(\partial_{μ} C_{2}^{μ ρ 00}) σ_{ε}^{''} - (\partial_{μ} M_{2}^{μ ρ 0}) σ_{ε}^{'} - M_{2}^{0 ρ 0} σ_{ε}^{''}] .$