  The possibility of a symmetry between gravitating and anti-gravitating
particles is examined. The properties of the anti-gravitating fields are
defined by their behavior under general diffeomorphisms. The equations of
motion and the conserved canonical currents are derived, and it is shown that
the kinetic energy remains positive whereas the new fields can make a negative
contribution to the source term of Einstein's field equations. The interaction
between the two types of fields is naturally suppressed by the Planck scale.
