On the renormalization of the quantum field theory of point-like monopoles and charges

The quantum field theory of point-like monopoles and charges is first formulated on a euclidean lattice for a convenient regularization. The regularization preserves the peculiar features of the theory, namely those related to the invariance and to the quantization condition. The partition function is expressed as a path integral over the particle's closed paths and the action is constructed in terms of arbitrary surfaces having those paths as boundaries. The possible divergences of the continuum limit are discussed, in particular the vacuum polarization ones. It is found that, although both the electric charge Q and the magnetic charge G are renormalized as Q = Zsub(Q)Qsub(R) and G = Zsub(G)Gsub(R), the quantization condition is preseverd by the renormalization i.e. Zsub(Q)Zsub(G) = 1 so that QG = Qsub(R)Gsub(R) = 2 πn. Due to the dual symmetry of the theory, then, for Q = G we get Zsub(Q) = Zsub(G) = 1. (orig.)