Thanks! Could you elaborate a bit more? I thought the invariance under diffeos would be equivalent to the gauge invariance of the, say, Maxwell Lagrangian.. in that case the change of the action is zero.
Hello!
I'm starting to study curved QFT and am slightly confused about the invariance of the Klein Gordon Lagrangian under a linear diffeomorphism.
This is $$L=\sqrt{-g}\left(g^{\mu\nu}\partial_\mu \phi \partial_\nu \phi-\frac{m^2}{2}\phi^2\right),$$
I don't see how ##g^{\mu\nu}\to...