  In the present paper, we investigate the ground state energy of a massless
scalar field and generation of topological mass by considering a
quasi-periodically identified Minkowski spacetime and the `half-Einstein
Universe', that is, an Einstein Universe where the massless scalar field
propagates under Dirichlet boundary condition. The analysis is performed
considering one and two-loop corrections to the effective potential in both
cases. Our results are compared with previous results found in literature.
