We present a method for studying the excitations of low-dimensional quantum
spin systems based on the Jordan-Wigner transformation. Using an extended
RPA-scheme we calculate the correlation function of neighboring spin flips
which well approximates the optical conductivity of Sr2CuO3. We
extend this approach to the two-leg S=1/2--ladder by numbering the spin
operators in a meander-like sequence. We obtain good agreement with the optical
conductivity of the spin ladder compound (La,Ca)14Cu24O41 for
polarization along the rungs. For polarization along the legs higher order
correlations are important to explain the weight of high-energy continuum
excitations and we estimate the contribution of 4-- and 6--fermion processes.Comment: 15 pages, 16 figure