A new 'dynamical mean-field theory' based approach for the Kondo lattice mo
del with quantum spins is introduced. The inspection of exactly solvable li
miting cases and several known approximation methods, namely the second-ord
er perturbation theory, the self-consistent CPA and finally a moment-conser
ving decoupling of the equations of motion, help in evaluating the new appr
oach. This comprehensive investigation gives some certainty to our results.
Whereas our method is somewhat limited in the investigation of the J < 0 m
odel, the results for J > 0 reveal important aspects of the physics of the
model: the energetically lowest states are not completely spin-polarized. A
band splitting, which occurs already for relatively low interaction streng
ths, can be related to distinct elementary excitations, namely magnon emiss
ion (absorption) and the formation of magnetic polarons. We demonstrate the
properties of the ferromagnetic Kondo lattice model in terms of spectral d
ensities and quasiparticle densities of states.