Bose-Einstein condensation in a constant magnetic field

We discuss the occurrence of Bose-Einstein condensation in systems of nonin teracting charged particles in three and one dimensions and in presence of an external magnetic field. In the one dimensional, as well as in the magne tic field cases, although not a critical temperature, a characteristic temp erature can be found, corresponding to the case in which the ground state d ensity becomes a macroscopic fraction of the total density. The case of rel ativistic charged scalar and vector particles is studied. The results give support to the existence of superconductivity in extremely strong magnetic fields, and lead to the prediction of superconductive-ferromagnetic behavio r in the vector field case, which might be of interest in condensed matter as well as in cosmology. Some features of the magnetization in the early un iverse are conjectured.