gauge invariance on curved space

[Elias Leite Mendonça]

Dear colleagues, greetings!

I am trying to demonstrate that a Lagrangian is gauge invariant. The model I am working on is based on a fully symmetric rank-2 field that I have called "h". This theory is set in a curved spacetime. The final result in the attached notebook (please focus only on section 3) should be zero, or at least a total derivative, however, it is not trivial to see this from the xAct output. Any suggestions on what else I could try? Or should I proceed with the calculations by hand?

All the best!

[Markus B. Fröb]

Dear Elias,

since you were working with an Einstein space, you also must replace the
Ricci tensor in your last equation by the corresponding multiple of the
metric. If you add
\[Delta]\[ScriptCapitalL]01 /. {RicciCD[a_, b_] :>
RicciScalarCD[]/dim metric[a, b]} // CollectTensors
to the very end, it will return 0 as required.

Best, Markus


Zitat von Elias Leite Mendonça <elias...@unesp.br>:

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