Manuscript X-C@3 · X-C-v3.tex · section · 2260f5f8

Switch factors displayed through second order

C4: completed test, three-term variation, and cancellation › Switch factors displayed through second order · lines 1083–1101

X-C@3#eq:N

Let $Q_{j}$ denote the unswitched positive Euler coefficients, and set $N_{j} = Q_{j} - L_{j, g}$ . Then

N_{1} [h] u N_{2} [h, k] u = (1 - g) Q_{1} [h] u - (\partial_{μ} g) a_{1}^{μν} [h] \partial_{ν} u, = (1 - g) Q_{2} [h, k] u - (\partial_{μ} g) A_{2}^{μν} [h, k] \partial_{ν} u .

These operators need not have compact coefficients. Their transformation differences below do.

Displayed formulas in this passage

X-C@3#eq:N · line 1089
$N_{1} [h] u N_{2} [h, k] u = (1 - g) Q_{1} [h] u - (\partial_{μ} g) a_{1}^{μν} [h] \partial_{ν} u, = (1 - g) Q_{2} [h, k] u - (\partial_{μ} g) A_{2}^{μν} [h, k] \partial_{ν} u .$