  All models of interacting electrons and spins can be reformulated as theories
of interacting Majorana fermions. We consider the Kondo lattice model that
admits a symmetric representation in terms of Majorana fermions. In the first
part of this work we study two variational states, which are natural in the
Majorana formulation. At weak coupling a state in which three Majorana fermions
tend to propagate together as bound objects is favored, while for strong
coupling a better description is obtained by having deconfined Majorana
fermions. This way of looking at the Kondo lattice offers an alternative
phenomenological description of this model. In the second part of the paper we
provide a detailed derivation of the discretized path integral formulation of
any Majorana fermion theory. This general formulation will be useful as a
starting point for further studies, such as Quantum Monte Carlo, perturbative
expansions, and Renormalization Group analysis. As an example we use this path
integral formalism to formulate a finite temperature variational calculation,
which generalizes the ground state variational calculation of the first part.
This calculation shows how the formation of three-body bound states of Majorana
fermions can be handled in the path integral formalism.

Strongly Correlated Electrons