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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeAug 31st 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexWhen 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? <a href="https://ncatlab.org/nlab/revision/diff/electromagnetic+field/64">diff</a>, <a href="https://ncatlab.org/nlab/revision/electromagnetic+field/64">v64</a>, <a href="https://ncatlab.org/nlab/show/electromagnetic+field">current</a>

   When formulated in the language of principal U(1)-bundles with connection, Maxwell’s equation reads .

   Since the electric current 3-form 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 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?

   diff, v64, current