nLab
field strength

In gauge theory cocycles in differential cohomology model gauge fields.

By definition, every differential cohomology theory ${\Gamma }^{•}(-)$ comes with a characteristic curvature form morphism

the (generalized) Chern character.

For $c\in {\Gamma }^{•}(X)$ a cocycle representing a gauge field in gauge theory, its image $F(c)\in {\Omega }^{•}(X)$ is the field strength of the gauge field. If we think of this cocycle as being (a generalization of) a connection on a bundle, this is essentially the curvature of that connection.

Often gauge fields are named after their field strength. For instance the field strength of the electromagnetic field is the $2$-form $F\in {\Omega }^2(X)$ whose components are the electric and the magnetic fields.