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We present a gauge and Lorentz invariant effective field theory model for theinteraction of a charged scalar matter field with a magnetic monopole source,described by an external magnetic current. The quantum fluctuations of themonopole field are described effectively by a strongly-coupled ``dual'' $U_{\rmd}(1)$ gauge field, which is independent of the electromagnetic $U_{\rm em}(1)$gauge field. The effective interactions of the charged matter with the monopolesource are described by a gauge invariant mixed Chern-Simons-like(Pontryagin-density) term between the two $U(1)$ gauge fields. The latterinteraction coupling is left free, and a Lattice study of the system isperformed with the aim of determining the phase structure of this effectivetheory. Our study shows that, in the spontaneously-broken-symmetry phase, themonopole source triggers, via the mixed Chern-Simons term, which is non-trivialin its presence, the generation of a dynamical singular configuration(magnetic-monopole-like) for the respective gauge fields. The scalar field alsobehaves in the broken phase in a way similar to that of the scalar sector ofthe `t Hooft-Polyakov monopole.

Effective Abelian Lattice Gauge Field Theories for scalar-matter-monopole interactions