A loop representation for the quantum Maxwell field

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Abstract
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 method, 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. The authors' own motivation, however, came from a non-perturbative approach to quantum gravity. The concrete results obtained in this work 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.
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