  We investigate the dynamical charge-charge correlation function and the
optical conductivity in weakly doped antiferromagnets using Mori-Zwanzig
projection technique. The system is described by the two-dimensional t-J model.
The arising matrix elements are evaluated within a cumulant formalism which was
recently applied to investigate magnetic properties of weakly doped
antiferromagnets. Within the present approach the ground state consists of
non-interacting hole quasiparticles. Our spectra agree well with numerical
results calculated via exact diagonalization techniques. The method we employ
enables us to explain the features present in the correlation functions. We
conclude that the charge dynamics at weak doping is governed by transitions
between excited states of spin-bag quasiparticles.
