  We describe projection operators in the matter sector of Witten's cubic
string field theory using modes on the right and left halves of the string.
These projection operators represent a step towards an analytic solution of the
equations of motion of the full string field theory, and can be used to
construct Dp-brane solutions of the string field theory when the BRST operator
Q is taken to be pure ghost, as suggested in the recent conjecture by Rastelli,
Sen and Zwiebach. We show that a family of solutions related to the sliver
state are rank one projection operators on the appropriate space of half-string
functionals, and we construct higher rank projection operators corresponding to
configurations of multiple D-branes.
