  The dynamics of magnetic vortices in the mixed state of d-wave
superconductors is affected by interaction with quasiparticles near the gap
nodes. We study this effect by computing the overlap of the ground state wave
functions of the nodal quasiparticles in a two-dimensional d-wave
superconductor as the ground state changes in response to the motion of the
vortex. We find that the overlap is strongly suppressed. This orthogonality
catastrophe is specific to a half-quantum vortex and disappears in the case of
a doubly-quantized vortex. This implies strong inhibition of the motion of
half-quantum vortices. The results allow us to develop a simple description of
the quantum vortex creep at low temperatures.
