  SU(2) lattice gauge theory is investigated where the traces of the Wilson
lines at any lattice point and along each direction is constrained to zero.
Hence, each of the lattice configurations possesses a vanishing density of
heavy (anti-) quarks. The results are compared with those of pure SU(2) gauge
theory which can be interpreted as the grand canonical realization of the heavy
quark theory where only the ensemble average of the heavy quark density
vanishes.
  The static quark anti-quark potential of the constrained theory is obtained
from (spatially smeared) Wilson loops at zero temperature. We find that the
potential coincides with that of pure SU(2) gauge theory (without constraints).
Hence, the familiar "running" of the lattice spacing with beta is recovered.
