Toward a theory of high-temperature superconductivity in the antiferromagnetically correlated cuprate oxides

We show that the retarded interaction between quasiparticiles on a 2D square lattice induced by the exchange of antiferromagnetic paramagnons leads uniquely to a transition to a superconducting state with dₓ²-y² symmetry. With a spin-excitation spectrum and a quasiparticle-paramagnon coupling determined by fits to normal-state experiments, we obtain high transition temperatures and energy-gap behaviors comparable to those measured for YBa₂{Cu}₃O₇, YBa₂{Cu}₃O6.63, and La1.85{Sr}0.15CuO₄.