The Casimir effect with quantized charged scalar matter in background   magnetic field
  We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged massive scalar matter field confined between two parallel plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirements that the operator of one-particle energy squared be self-adjoint and positive definite. We show that, in the case of a weak magnetic field and a small separation of the plates, the Casimir force is either attractive or repulsive, depending on the choice of a boundary condition. In the case of a strong magnetic field and a large separation of the plates, the Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates. 
Yu. A. Sitenko and S. A. Yushchenko
hep-th math-ph math.MP quant-ph