  The intimate connection between antiferromagnetism and superconductivity is
at the core of high-temperature superconductivity. Here, we put forward the
projected BCS theory for the unification of antiferromagnetism at half filling
and strongly correlated superconductivity at moderate doping. Specifically, it
is shown that the projected BCS theory provides excellent trial states for the
exact ground states of the $t$-$J$ model in the square lattice, generating the
unified phase diagram as a continuous function of hole concentration. Precisely
capturing antiferromagnetism at half filling, which is ultimately a consequence
of the strong correlation between Cooper pairs, the projected BCS theory is
able to produce better trial states for strongly correlated superconductivity
at moderate doping than the resonating valence bond state. Finally, we discuss
various ramifications of the projected BCS theory.
