Condensation and Magnetization of the Relativistic Bose Gas

We present a simple proof of the absence of Bose–Einstein condensation of a relativistic boson gas, in any finite local magnetic field in less than five dimensions. We show that the relativistic charged boson gas exhibit 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. The result is discussed in the context of kaon condensation in neutron stars.