  We derive a condition for the existence of completely or exponentially
localised Majorana bound states (with the potential for non-Abelian statistics)
in a generic many-body system. We discuss the relationship between the
existence of these operators and the protection of the ground state degeneracy
from local perturbations. We use our methods to study the exponential decay of
the Majorana bound states in the non-interacting Kitaev chain, finding complete
agreement between our many-body calculation and single-particle results. We
then apply these results to various interacting systems which have previous
evidence for Majorana bound states.
