Condensation and magnetization of the relativistic Bose gas

We show that the relativistic charged scalar boson gas exhibits a genuine Meissner-Ochsenfeld effect of the Schafroth form at fixed supercritical density. As in the well-known non-relativistic case, this total expulsion of a magnetic field is caused by the condensation of the Bose gas at vanishing magnetic field. In the course of these considerations, we present alternative proofs of the absence of Bose-Einstein condensation of a relativistic scalar boson gas, in any finite local magnetic field in less than five dimensions. The results are discussed in the context of kaon condensation in neutron stars.