Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Application to gauge theory
In gauge theory of higher abelian Yang-Mills theory type, where field configurations on some manifold are circle n-bundles with connection , the magnetic flux of the field configuration through a -dimensional closed manifold is
\Phi_\sigma(\nabla) = \int_\Sigma F_\nabla
where is the curvature -form.
If is contractible in , hence if there is a such whose boundary is then this is the (higher) magnetic charge enclosed by .
Revised on January 11, 2013 00:28:31
by Urs Schreiber