The local switched Noether defect

Displayed formulas in this passage

• VI@1#eq:local-noether-defect · line 2582

  $$\begin{array}{rl}{\delta }_0{V_1}^{\mathrm{m}}(g;h,\phi )& =\int g{T}^{\mu \nu }{\partial }_{\mu }{\xi }_{\nu }{\mathrm{d}}^{4}x\\ & =-\int g(P\phi )X_{\xi }\phi {\mathrm{d}}^{4}x-\int ({\partial }_{\mu }g)T^{\mu \nu }{\xi }_{\nu }{\mathrm{d}}^{4}x.\end{array}$$

• VI@1#eq:switched-noether · line 2599

  $${\delta }_0{V_1}^{\mathrm{m}}+{{\delta }_1}^g{S}_0^{\mathrm{m}}=-\int ({\partial }_{\mu }g)T^{\mu \nu }{\xi }_{\nu }{\mathrm{d}}^{4}x.$$

• unlabeled · line 2578

  $${\partial }_{\mu }{T}^{\mu \nu }=(P\phi ){\partial }^{\nu }\phi .$$

• unlabeled · line 2593

  $${{\delta }_1}^g{S}_0^{\mathrm{m}}=\int (P\phi )g{X}_{\xi }\phi {\mathrm{d}}^{4}x,$$