Manuscript X-G@1 · X-G.tex · section · 01566e14

The nonlinear kinematics and background ghost operator

The nonlinear kinematics and background ghost operator · lines 793–815

X-G@1#eq:nonlinear

Write

q = q ˉ + κh .

The complete formal background may include $κ^{2} k_{cl}$ ; it is held fixed under the quantum-gauge differential.

Define

s h s c^{μ} = L_{c} q ˉ + κ L_{c} h, = κ c^{ν} \partial_{ν} c^{μ}, s ϕ s c ˉ = κ c^{μ} \partial_{μ} ϕ, = b, s b = 0.

Odd coefficients are placed on the left in the component Lie-derivative formulas.

Displayed formulas in this passage

X-G@1#eq:nonlinear · line 804
$s h s c^{μ} = L_{c} q ˉ + κ L_{c} h, = κ c^{ν} \partial_{ν} c^{μ}, s ϕ s c ˉ = κ c^{μ} \partial_{μ} ϕ, = b, s b = 0.$
unlabeled · line 797
$q = q ˉ + κh .$