On the possibility of Bose-Einstein condensation in a solid

We treat the question of the existence of Bose-Einstein condensation (BEC) in Bose lattice systems. Simple examples are constructed that do display BEC while having a lattice symmetry. It is suggested, however, that these systems are not crystals in the ordinary sense. When a more conventional definition of a lattice is employed, we generalize the proof of Matsuda and Tsuneto that BEC does not exist in a Bose lattice, for a wider class of wave functions including two-body correlations. A solid with a finite vacancy concentration can display BEC, which is related to the BEC in the vacancy gas. We clarify the relation between BEC of vacancies and particles.