Hello everyone, I would like to know if anyone knows what is the inner product for vector fields ##A_\mu## in curved space-time. Is it just:(adsbygoogle = window.adsbygoogle || []).push({});

$$

(A_\mu,A_\mu)=\int d^4x A_\mu A^\mu =\int d^4x g^{\mu\nu}A_\mu A_\nu

$$

? Do I need extra factors of the metric?

Thanks!

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# Inner product for vector field in curved background

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