  The ground states and excitations of two-dimensional insulating and doped
Mott insulators are described by a bond operator formalism. While the method
represents the degrees of freedom of an arbitrary antiferromagnet exactly, it
is especially suited to systems in which there is a natural pairing of sites
into bonds, as in states with spontaneous or explicit spin-Peierls order (or
bond-centered charge order). In the undoped insulator, as discussed previously,
we obtain both paramagnetic and magnetically-ordered states. We describe the
evolution of superconducting order in the ground state with increasing
doping--at low doping, the superconductivity is weak, can co-exist with
magnetic order, and there are no gapless spin 1/2 fermionic excitations; at
high doping, the magnetic order is absent and we obtain a BCS d-wave
superconductor with gapless spin 1/2, nodal fermions. We present the critical
theory describing the onset of these nodal fermionic excitations. We discuss
the evolution of the spin spectrum, and obtain regimes where a spin 1 exciton
contributes a sharp resonance in the dynamic spin susceptiblity. We also
discuss the experimental consequences of low-energy, dynamically fluctuating,
spin-Peierls order in an isotropic CuO_2 plane--we compute consequences for the
damping and dispersion of an optical phonon involving primarily the O ions, and
compare the results with recent neutron scattering measurements of phonon
spectra.
