So F is essentially the analog of the metric?
Only two of Maxwell's Equations can be derived from varying the action of QED (eq. 1)
To obtain the others, we need Fμν to satisfy the Bianchi Identity (eq. 2)
This implies that Fμν represents a 𝒄𝒖𝒓𝒗𝒂𝒕𝒖𝒓𝒆
This curvature is in a space called a "vector bundle"pic.twitter.com/qlflapqh0G
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Not quite. Fμν is a tensor that has a non vanishing Riemann curvature tensor on the vector bundle
End of conversation
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Right yes, because classical current is the Noether flow of the stress-energy of the electromagnetic field tensor. This amounts to requiring that the field generates consistent geodesics, which in turn amounts to requiring that the field obeys classical local conservation laws.
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