  We describe the influence of the gapless, nodal, fermionic quasiparticles of
a two-dimensional d-wave superconductor on the motion of vortices. A continuum,
functional formalism is used to obtain the effective vortex action, after the
fermions have been integrated out. At zero temperture (T), the leading terms in
the vortex action retain their original form, with only a finite
renormalization of the vortex effective mass from the fermions. A universal
"sub-ohmic" damping of the vortex motion is also found. At T>0, we find a
Bardeen-Stephen viscous drag term, with a universal co-efficient which vanishes
as ~T^2. We present a simple scaling interpretation of our results, in which
quantum-critical Dirac fermions respond to a moving point singularity. Our
results appear to differ from those of the semiclassical theory, which obtains
more singular corrections to a vortex mass appearing in transport equations.
