  The properties of vortices in Josephson junction arrays are investigated in
the quantum regime near the superconductor-insulator transition. We derive and
study an effective action for vortex dynamics that is valid in the region where
the charging energy is comparable to the Josephson coupling energy. In the
superconducting phase the onset of quantum effects reduces the vortex mass and
depinning current. In the case of long range Coulomb interaction between Cooper
pairs we find that as the transition is approached, the velocity window in
which ballistic vortex motion is possible grows. At the
superconductor-insulator transition the vortex mass vanishes and vortices and
spinwaves decouple. In the case of on-site Coulomb repulsion (which is of
relevance for superconducting granular films) the vortex mass it is sample-size
dependent in the superconducting phase, but stays finite at the critical point
where it is scale invariant. The relation of our work to experiment is
discussed.
