nLab
flux

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Differential cohomology

\infty-Chern-Weil theory

Contents

Definition

In gauge theory of higher abelian Yang-Mills theory type, where field configurations on some manifold XX are circle n-bundles with connection \nabla, the magnetic flux of the field configuration through a (n+1)(n+1)-dimensional closed manifold ΣX\Sigma \hookrightarrow X is

Φ σ()= ΣF , \Phi_\sigma(\nabla) = \int_\Sigma F_\nabla \,,

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

Properties

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

Revised on January 11, 2013 00:28:31 by Urs Schreiber (82.113.98.146)