  The effective Hamiltonian of strongly correlated electrons on a square
lattice is replaced by a renormalised Hamiltonian and the factors that
renormalise the kinetic energy of holes and the Heisenberg spin-spin coupling
are calculated using a Gutzwiller approximation scheme. The accuracy of this
renormalisation procedure is tested numerically and found to be qualitatively
excellent. Within the scheme a resonant valence bond (RVB) wavefunction is
found at half-filling to be lower in energy than the antiferromagnetic state.
If the wavefunction is expressed in fermion operators, local SU(2) and U(l)
invariance leads to a redundancy in the representation. The introduction of
holes removes these local invariances and we find that a d-wave RVB state is
lowest in energy. This state has a superconducting order parameter whose
amplitude is linear in the density of holes.
