Manuscript XI-E@1 · XI-E.tex · section · 46e55514

The correct switching support

Route 2: localized support and the scalar-response frame › The correct switching support · lines 1201–1221

XI-E@1#eq:generaldefect

For a compact interior $ξ$ , the free scalar identity gives

A_{1} [K ξ; ϕ] = W_{f} (2 ξ; ϕ) + \int f (g - 1) X_{ξ} ϕ d^{4} x - \int f E_{m}^{R} ([P_{m}, g] X_{ξ} ϕ + (\partial_{μ} g) a_{1}^{μν} [K ξ] \partial_{ν} ϕ) d^{4} x, P_{m} ϕ = 0,

where

[P_{m}, g] u = (□ g) u + 2 (\partial^{μ} g) \partial_{μ} u .

Displayed formulas in this passage

XI-E@1#eq:generaldefect · line 1205
$A_{1} [K ξ; ϕ] = W_{f} (2 ξ; ϕ) + \int f (g - 1) X_{ξ} ϕ d^{4} x - \int f E_{m}^{R} ([P_{m}, g] X_{ξ} ϕ + (\partial_{μ} g) a_{1}^{μν} [K ξ] \partial_{ν} ϕ) d^{4} x, P_{m} ϕ = 0,$
unlabeled · line 1218
$[P_{m}, g] u = (□ g) u + 2 (\partial^{μ} g) \partial_{μ} u .$