Manuscript VII-A-ST@1 · VII-A-ST.tex · section · c39a67a3

The named plateau Einstein–scalar coupling jet

The named plateau Einstein–scalar coupling jet · lines 1098–1128

VII-A-ST@1#eq:Einstein-normalization

The off-shell intertwiner does not require gravitational equations. To state its intended on-shell restriction, fix the normalization

G_{μν} [γ] = κ^{2} T_{μν} [γ, ϕ] .

This is VII-A's normalization. A coefficient such as the $1/4$ used in another action convention must not be transferred without rescaling the coupling.

Define

G [η + κh + κ^{2} k] = κ G^{(1)} [h] + κ^{2} (G^{(1)} [k] + G^{(2)} [h, h]) (mod κ^{3}) .

The differential definition is given in Appendix app:curvature. The leading stress tensor is

T^{(0)}_{μν} [ϕ_{0}] = \partial_{μ} ϕ_{0} \partial_{ν} ϕ_{0} - \frac{1}{2} η_{μν} (\partial^{ρ} ϕ_{0} \partial_{ρ} ϕ_{0} + m^{2} ϕ_{0}^{2}) .

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VII-A-ST@1#eq:Einstein-normalization · line 1104
$G_{μν} [γ] = κ^{2} T_{μν} [γ, ϕ] .$
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$G [η + κh + κ^{2} k] = κ G^{(1)} [h] + κ^{2} (G^{(1)} [k] + G^{(2)} [h, h]) (mod κ^{3}) .$
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$T^{(0)}_{μν} [ϕ_{0}] = \partial_{μ} ϕ_{0} \partial_{ν} ϕ_{0} - \frac{1}{2} η_{μν} (\partial^{ρ} ϕ_{0} \partial_{ρ} ϕ_{0} + m^{2} ϕ_{0}^{2}) .$

The named plateau Einstein–scalar coupling jet

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