Where switch derivatives actually occur

Displayed formulas in this passage

• XI-A@1#eq:Ephi · line 730

  $$E_{\varphi }=\frac{\delta S_{\mathrm{inv}}}{\delta \varphi }=-\left(P_m+\kappa {\mathsf{V}}_{1,g}+{\kappa }^2{\mathsf{V}}_{2,g}\right)\varphi +O({\kappa }^3),$$

• XI-A@1#eq:scalar-switch · line 737

  $$\begin{array}{rl}{\mathsf{V}}_{1,g}\varphi & =g\left[{\partial }_{\mu }({a_1}^{\mu \nu }{p}_{\nu })+m^2{b}_1\varphi \right]+({\partial }_{\mu }g){a_1}^{\mu \nu }{p}_{\nu },\\ {\mathsf{V}}_{2,g}\varphi & =g\left[{\partial }_{\mu }({a_2}^{\mu \nu }{p}_{\nu })+m^2{b}_2\varphi \right]+({\partial }_{\mu }g){a_2}^{\mu \nu }{p}_{\nu }.\end{array}$$

• unlabeled · line 747

  $${\partial }_{\mu }(g{T}_0^{\mu \nu })=g(P_m\varphi ){\partial }^{\nu }\varphi +({\partial }_{\mu }g){T_0}^{\mu \nu }.$$