  Fermionic mean-field theory and variational Monte Carlo calculations are
employed to shed light on the possible uniform ground states of the Heisenberg
model on the pyrochlore lattice. Among the various flux configurations, we find
the chiral spin states carrying \pm pi/2 flux through each triangular face to
be the most stable both within the mean-field theory and the projected
wave-function studies. Properties of the spin-spin correlation function and the
chirality order parameter are calculated for the projected wave functions.
Mean-field band structures are examined.
