In a paper about field theory in curved spacetime, an author says that the Lagrangian density for a free scalar particle is(adsbygoogle = window.adsbygoogle || []).push({});

[itex]L = \sqrt{-g} ((\nabla_\mu \Phi)(\nabla^\mu \Phi) - m^2 \Phi^2)[/itex]

Is there a simple explanation for why this is scaled by [itex]\sqrt{-g}[/itex]?

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# Why the square-root of the metric

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