SIMPLE CRITERION FOR THE OCCURRENCE OF BOSE-EINSTEIN CONDENSATION ANDTHE MEISSNER-OCHSENFELD EFFECT

We examine the occurrence of Bose-Einstein condensation in both nonrel ativistic and relativistic systems with no self-interactions in a gene ral setting. A simple condition for the occurrence of Bose-Einstein co ndensation is given. We show that condensation can occur only if q gre ater than or equal to 3, where q is the dimension associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonr elativistic systems or the spatial part of the Klein-Gordon operator f or relativistic systems. Furthermore we show that the criterion for th e appearance of the Meissner-Ochsenfeld effect is closely connected wi th that for the appearance of Bose-Einstein condensation.