Maxwell equations

From DispersiveWiki

The Maxwell equations are the special case of the Yang-Mills equations when the gauge group is just the abelian circle group U(1). These equations take the form

where F is the curvature of a U(1) connection :

Note that the Bianchi identity also gives the equation

which is also traditionally given as one of the Maxwell equations.

In the presence of a current , the Maxwell equations now take the form

(after normalizing various physical constants).

The Maxwell equations are linear. However, by coupling the Maxwell equations to a scalar field one obtains the nonlinear Maxwell-Klein-Gordon equations.