We prove some algebraic relations on the translationally invariant solutions and the lump solutions in vacuum string field theory. We show that up to the subtlety at the midpoint the definition of the half-string projectors of the known sliver solution can be generalized to other solutions. We also find that we can embed the translationally invariant solution into the matrix equation of motion ...

I wish to address both a substantive and a methodological issue in this chapter. Substantively, I will discuss the process of state disintegration and reconstruction. Here, I will draw on the experience of Eastern Europe following the collapse of Communism. Today, more than twenty new states occupy the territories formerly held by the Soviet Union, Yugoslavia, and Czechoslovakia. Furthermore, t...

This is a brief review of vacuum string field theory, a new approach to open string field theory based on the stable vacuum of the tachyon. We discuss the sliver state explaining its role as a projector in the space of half-string functionals. We review the construction of D-brane solutions in vacuum string field theory, both in the algebraic approach and in the more general geometrical approac...