Classical loop actions of gauge theories

Since the first attempt to quantize gauge theories and gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply to the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing us to do Monte Carlo calculations in a gauge-invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ‘‘confining phase.’’