Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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