  This work is concerned with two-spin-1/2-fermion relativistic quantum
mechanics, and it is about the construction of one-particle projectors using an
inherently two(many)-particle, `explicitly correlated' basis representation,
necessary for good numerical convergence of the interaction energy. It is
demonstrated that a faithful representation of the one-particle operators,
which appear in intermediate but essential computational steps, can be
constructed over a many-particle basis set by accounting for the full Hilbert
space beyond the physically relevant anti-symmetric subspace. Applications of
this development can be foreseen for the computation of quantum-electrodynamics
corrections for a correlated relativistic reference state and high-precision
relativistic computations of medium-to-high-$Z$ helium-like systems, for which
other two-particle projection techniques are unreliable.
