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When formulated in the language of principal U(1)-bundles with connection, Maxwell’s equation reads $d*F=j$.
Since the electric current 3-form $j$ is closed, this makes me think it could, more generally, be the curvature 3-form of some bundle gerbe with connection (the “electric current bundle gerbe”).
The equation $d*F=j$ would then somehow be related to trivializing this bundle gerbe.
Has something like this been considered in the literature?
I am also not sure how the Hodge star is supposed to interact with differential cohomology, are there any sources that cover this?
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