Casimir forces in models with non-trivial topology

Abstract

The Casimir forces, acting on the parallel plates in models with the compact subspace are investigated for the case of a scalar field. The field obeys the Robin boundary conditions on the plates. Depending on the values of the coefficients in the boundary conditions, the forces can be either attractive or repulsive. In models with a homogeneous compact subspace, they are the same for both the plates. In special cases of the Dirichlet and Neumann boundary conditions, the Casimir forces are attractive. Proceeding from general results, two particular cases with the subspaces S¹ and S² are considered.