  We present a new approach to static and dynamical properties of holes and
spins in weakly doped antiferromagnets in two dimensions. The calculations are
based on a recently introduced cumulant approach to ground--state properties of
correlated electronic systems. The present method allows to evaluate hole and
spin--wave dispersion relations by considering hole or spin excitations of the
ground state. Usually, these dispersions are found from time--dependent
correlation functions. To demonstrate the ability of the approach we first
derive the dispersion relation for the lowest single hole excitation at
half--filling. However, the main purpose of this paper is to focus on the
mutual influence of mobile holes and spin waves in the weakly doped system. It
is shown that low-energy spin excitations strongly admix to the ground--state.
The coupling of spin waves and holes leads to a strong suppression of the
staggered magnetization which can not be explained by a simple rigid--band
picture for the hole quasiparticles. Also the experimentally observed doping
dependence of the spin--wave excitation energies can be understood within our
formalism.
