Manuscript XIII-B@1 · XIII-B.tex · section · b8a5c0f5

The interaction entry

B5: the free differential, displayed without a defect › The interaction entry · lines 1176–1196

XIII-B@1#eq:sV, XIII-B@1#eq:sV-shell

Using symmetry of $T_{0}$ and compact integration by parts,

s_{0} V_{g} = - \frac{1}{2} \int g (R c)_{μν} T_{0}^{μν} d^{4} x = \frac{1}{2} \int c_{ν} ((\partial_{μ} g) T_{0}^{μν} + g (P_{m} ϕ) \partial^{ν} ϕ) d^{4} x .

On the free scalar shell,

s_{0} V_{g} = \frac{1}{2} \int c_{ν} (\partial_{μ} g) T_{0}^{μν} d^{4} x .

The ghost need not be supported in $W$ , so the switching term does not vanish merely because $g = 1$ on $W$ . There is no coordinate ramp in this vertex.

Displayed formulas in this passage

XIII-B@1#eq:sV · line 1179
$s_{0} V_{g} = - \frac{1}{2} \int g (R c)_{μν} T_{0}^{μν} d^{4} x = \frac{1}{2} \int c_{ν} ((\partial_{μ} g) T_{0}^{μν} + g (P_{m} ϕ) \partial^{ν} ϕ) d^{4} x .$
XIII-B@1#eq:sV-shell · line 1188
$s_{0} V_{g} = \frac{1}{2} \int c_{ν} (\partial_{μ} g) T_{0}^{μν} d^{4} x .$