  We present a gauge and Lorentz invariant model for the scattering of matter
off magnetic poles, which justifies the presence of velocity-dependent magnetic
charges as an effective description of either the behaviour of monopoles in
scattering with matter or their production from matter particles at colliders.
Hence, in such an approach, perturbativity of the magnetic charge is ensured
for relative low velocities of monopoles with respect to matter particles. The
model employs a ${\rm U(1)}_{\rm weak} \times {\rm U(1)}_{\rm strong}$
effective gauge field theory under which electrons and monopoles (assumed to be
fermions) are appropriately charged. The non-perturbative quantum effects of
the strongly coupled sector of the theory lead to dressed effective couplings
of the monopole/dyon with the electromagnetic photon, due to non-trivial
wave-function renormalization effects. For slowly-moving monopole/dyons, such
effects lead to weak coupling, thus turning the bare non-perturbative magnetic
charge, which is large due to the Dirac/Schwinger quantization rule, into a
perturbative effective, velocity-("$\beta$")-dependent magnetic coupling. Our
work thus offers formal support to previous conjectural studies, employing
effective U(1)-electromagnetic gauge field theories for the description of
monopole production from Standard Model matter, which are used in contemporary
collider searches of such objects. This work necessarily pertains to composite
monopoles, as seems to be the case of all known monopoles so far, that are
solutions of specific particle physics models. This is a consequence of the
fact that the wave-function renormalization of the (slowly-moving) monopole
fermion turns out to violate unitarity bounds that would characterise
asymptotic elementary particle states.
