Does any one know how to write the Maxwell equations as an equation on a principal $U(1)$-bundle? 


In Freed & Uhlenbeck's *Instantons and Four manifolds*, the authors claim that the Maxwell equations can be written in a gauge theoretic way: the electro-magnetic field can be viewed as the curvature $F$ of a $U(1)$-bundle on the 4-dimensional Lorentz manifold, and the Maxwell equations are equivalent to $d^∗\_A(F)=0$, where A is the connection. Does anyone have a reference for this statement? I just want to have a look at the proof and see how everything matches.



Gauge-theoretic formulation of Maxwell equations
I don't have my copy handy, but I think this is all worked out in chapter 2 of Naber's "Topology, Geometry, and Gauge Fields: Interactions". The book is essentially a textbook on differential geometry with a view toward physics, so the exposition is very detailed; I just can't remember how much time is spent on Maxwell's equations.


