  We highlight the properties of a simple model (contained in our recent work)
of the quantum dynamics of a single point vortex interacting with the nodal
fermionic quasiparticles of a d-wave superconductor. We describe the
renormalization of the vortex motion by the quasiparticles: at T=0, the
quasiparticles renormalize the vortex mass and introduce only a weak sub-Ohmic
damping. Ohmic (or `Bardeen-Stephen' damping) appears at T>0, with the damping
co-efficient vanishing ~ T^2 with a universal prefactor. Conversely, quantum
fluctuations of the vortex renormalize the quasiparticle spectrum. A point
vortex oscillating in a harmonic pinning potential has no zero-bias peak in the
electronic local density of states (LDOS), but has small satellite features at
an energy determined by the pinning potential. These are proposed as the origin
of sub-gap LDOS peaks observed in scanning tunneling microscopic studies of the
LDOS near a vortex.
