In this paper we define invariants of Hamiltonian group actions
for central regular values of the moment map. The key hypotheses
are that the moment map is proper and that the ambient
manifold is symplectically aspherical. The invariants are based
on the symplectic vortex equations. Applications include an
existence theorem for relative periodic orbits, a computation for
circle actions on a complex vector space, and a theorem
about the relaton between the invariants introduced here and the
Seiberg-Witten invariants of a product of a Riemann surface
with a two-sphere.