Manuscript X-E-ST@1 · X-E-ST.tex · definition · 44614221

Definition: Coupled invariant two-jet

E2: plateau covariance and the coupled-jet obstruction › The invariant two-jet surface · lines 834–851

X-E-ST@1#def:coupled, X-E-ST@1#eq:coupled

For a specified free scalar input $ϕ_{0}$ , let $C^{[2]}_{ϕ_{0}}$ consist of

q = η + κh + κ^{2} k, ϕ = ϕ_{0} + κ ϕ_{1} + κ^{2} ϕ_{2}

satisfying

J_{q} G [q] - κ^{2} g J_{q} T [q, ϕ] = O (κ^{3}), E_{ϕ} [q, ϕ] = O (κ^{3}) .

Coordinate data remain (eq:coordinates). No gauge-fixed equation is substituted for the first condition.

Displayed formulas in this passage

X-E-ST@1#eq:coupled · line 843
$J_{q} G [q] - κ^{2} g J_{q} T [q, ϕ] = O (κ^{3}), E_{ϕ} [q, ϕ] = O (κ^{3}) .$
unlabeled · line 838
$q = η + κh + κ^{2} k, ϕ = ϕ_{0} + κ ϕ_{1} + κ^{2} ϕ_{2}$