  Quantization of the free Maxwell field in Minkowski space is carried out
using a loop representation and shown to be equivalent to the standard Fock
quantization. Because it is based on coherent state methods, this framework may
be useful in quantum optics. It is also well-suited for the discussion of
issues related to flux quantization in condensed matter physics. Our own
motivation, however, came from a non-perturbative approach to quantum gravity.
The concrete results obtained in this paper for the Maxwell field provide
independent support for that approach. In addition, they offer some insight
into the physical interpretation of the mathematical structures that play,
within this approach, an essential role in the description of the quantum
geometry at Planck scale.
