SUPERCONDUCTIVITY OF THE BOSE-GAS

We investigate the magnetic properties of the ideal Bose gas in both t he relativistic and nonrelativistic regimes, and demonstrate its remar kable behavior as a superconductor, where: it expels totally an extern al homogeneous field, and also a new phenomenon, which we call superdi amagnetism, where the gas very nearly does so. These two phenomena are shown to exist in two distinct temperature regimes for both the nonre lativistic and relativistic gases, and are revealed by a careful consi deration of the analytic structure of the thermodynamic potential of t he system, accessible by the powerful method of the Mellin integral tr ansform. We also comment on other approaches to this problem which hav e recently appeared.