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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 $d*F=j$.

   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?

   diff, v64, current