SIMPLE CRITERION FOR THE OCCURRENCE OF BOSE-EINSTEIN CONDENSATION

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 can be given if we adopt generalized C-functions to define the quantum theory. We show that the crucial feature governing Bose-Ei nstein condensation is the dimension q associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativi stic systems. In either case Bose-Einstein condensation can only occur if q greater than or equal to 3.