BOSE-EINSTEIN CONDENSATION AS SYMMETRY-BREAKING IN COMPACT CURVED SPACETIMES

We examine Bose-Einstein condensation as a form of symmetry breaking i n the specific model of the Einstein static universe. We show that sym metry breaking never occurs in the sense that the chemical potential m u never reaches its critical value. This leads us to some statements a bout spaces of finite volume in general. In an appendix we clarify the relationship between the standard statistical mechanical approaches a nd the field theory method using zeta functions.