Particle-number projection and the density functional theory

In the framework of the density functional theory for superconductors, we study the restoration of the particle-number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed. Both are related to the fact that neither the many-body Hamiltonian nor the wave function of the system appear explicitly in the density functional theory. Similar obstacles are encountered in self-consistent theories utilizing density-dependent effective interactions.