  We use the Shadow Wave Function formalism as a convenient model to study the
fermion sign problem affecting all projector Quantum Monte Carlo methods in
continuum space. We demonstrate that the efficiency of imaginary time
projection algorithms decays exponentially with increasing number of particles
and/or imaginary-time propagation. Moreover, we derive an analytical expression
that connects the localization of the system with the magnitude of the sign
problem, illustrating this prediction through some numerical results. Finally,
we discuss the fermion sign problem computational complexity and methods for
alleviating its severity.
