We consider a two-dimensional array of ultrasmall superconducting grai
ns, weakly coupled by Josephson junctions with large charging energy.
We start from an effective action based on a microscopic tunneling Ham
iltonian, which includes quasiparticle degrees of freedom, and study t
he resulting dissipative dynamics of quantum vortices. The equation of
motion for a single vortex is deduced, and compared with a commonly a
dopted phenomenological model.