  The goal of this paper is to give a new proof of a theorem of Meng and Taubes
that identifies the Seiberg-Witten invariants of 3-manifolds with Milnor
torsion. The point of view here will be that of topological quantum field
theory. In particular, we relate the Seiberg-Witten equations on a 3-manifold
with the Abelian vortex equations on a Riemann surface. These techniques also
give a new proof of the surgery formula for the Casson invariant, interpreted
as an invariant of a homology S^2 x S^1.
