  The $t-J$ Hamiltonian is studied in a mean-field approximation by taking into
account antiferromagnetic and d-wave pairing correlations. Considering the
presence of antiferromagnetic fluctuations, the weaknesses of a mean-field
approximation and the limitation of the $t-J$ model near half-filling, we give
a new interpretation to the slave boson mean-field theory of the $t-J$ model.
We argue that due to phase coherence-breaking antiferromagnetic fluctuations
and quantum fluctuations, superconducting long-range order does not appear
strictly in two dimensions. $T_{c}$ resulting from interlayer pairing hopping
can lead to a universal relation, when $T_{c}$ is scaled by $T^{max}_{c}$.
Systematic reduction of superfluid density and increase of
$(\Delta_{d})_{max}/K_{B}T_{c}$ ratio below and near optimal doping have their
natural explanation in our picture. A crossover temperature $T^{0}$ found in
some of magnetic experiments such as NMR is also easily understood in the
present framework.
