Manuscript VI@1 · VI.tex · section · b5b60afb

Why the first-order matching claim needs qualification

Bare dressing, solution coefficients, and external response › Why the first-order matching claim needs qualification · lines 1351–1372

VI@1#eq:candidate-dressed

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Three expressions must be distinguished:

bare dressing: external forced response: candidate dressed response: - \int f X_{w [h]} ϕ_{0}, \int f ϕ_{1, g} [h, ϕ_{0}], \int f (ϕ_{1, g} [h, ϕ_{0}] - X_{w [h]} ϕ_{0}) .

The first two are not equal in general. The third is the object whose switch compatibility must be checked.

Even when a special harmonic restriction makes $w [h] = 0$ , equality of two displayed expressions on that restriction is not a proof that their constructions intertwine the gauge actions on a larger domain.

Figure fig:VI-three-coefficients distinguishes bare, solution-jet, and switched-response coefficients.

Displayed formulas in this passage

VI@1#eq:candidate-dressed · line 1354
$bare dressing: external forced response: candidate dressed response: - \int f X_{w [h]} ϕ_{0}, \int f ϕ_{1, g} [h, ϕ_{0}], \int f (ϕ_{1, g} [h, ϕ_{0}] - X_{w [h]} ϕ_{0}) .$

Nearby in this section

figure: Three coefficient constructions