  Using a canonical transformation it is possible to faithfully represent the
Kondo lattice model in terms of Majorana fermions. Studying this representation
we discovered an exact mapping between the Kondo lattice Hamiltonian and a
Hamiltonian describing three spinless fermions interacting on a lattice. We
investigate the effectiveness of this three fermion representation by
performing a zero temperature mean-field study of the phase diagram at
different couplings and fillings for the one-dimensional case, focusing on the
appearance of ferromagnetism. The solutions agree in many respects with the
known numerical and analytical results. In particular, in the ferromagnetic
region connected to the solution at zero electron density, we have a
quantitative agreement on the value of the commensurability parameter
discovered in recent DMRG (in one dimension) and DMFT (in infinite dimensions)
simulations; furthermore we provide a theoretical justification for it,
identifying a symmetry of the Hamiltonian. This ferromagnetic phase is
stabilized by the emergence of a spin-selective Kondo insulator that is
described quite conveniently by the three spinless fermions. We discovered also
a different ferromagnetic phase at high filling and low couplings. This phase
resembles the RKKY ferromagnetic phase existing at vanishing filling, but it
incorporates much more of the Kondo effect, making it energetically more
favorable than the typical spiral (spin ordered) mean field ground states. We
believe that this second phase represents a prototype for the strange
ferromagnetic tongue identified by numerical simulations inside the
paramagnetic dome. At the end of the work we also provide a discussion of
possible orders different from the ferromagnetic one. In particular at
half-filling, where we obtain as ground state at high coupling the correct
Kondo insulating state.
