Magnetic Monopole in the Loop Representation

We quantize, within the Loop Representation formalism, the electromagnetic field in the presence of a static magnetic pole. It is found that loop-dependent physical wave functionals acquire a topological dependence on the surfaces bounded by the loop. This fact generalizes what occurs in ordinary quantum mechanics in multiply connected spaces. When Dirac’s quantization condition is satisfied, the dependence on the surfaces disappears, together with the influence of the monopole on the quantized electromagnetic field.