nLab
flux
Contents
Context
Physics
Differential cohomology
differential cohomology

Ingredients
Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Fiber integration
Application to gauge theory
$\infty$ -Chern-Weil theory
Contents
Definition
In gauge theory of higher abelian Yang-Mills theory type, where field configurations on some manifold $X$ are circle n-bundles with connection $\nabla$ , the magnetic flux of the field configuration through a $(n+1)$ -dimension al closed manifold $\Sigma \hookrightarrow X$ is

$\Phi_\sigma(\nabla) = \int_\Sigma F_\nabla
\,,$

where $F_\nabla$ is the curvature $(n+1)$ -form.

Properties
If $\Sigma$ is contractible in $X$ , hence if there is a $\hat \Sigma \hookrightarrow X$ such whose boundary is $\partial \hat \Sigma = \Sigma$ then this is the (higher) magnetic charge enclosed by $\Sigma$ .

Last revised on March 24, 2019 at 10:34:34.
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