The Casimir effect with quantized charged scalar matter in background magnetic field

Abstract

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 requirement 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.

Casimir effect with quantized charged spinor matter in background magnetic field

“…As to the remaining part, it is calculated in the cases of the antiperiodic boundary condition [19,21] and the MIT bag boundary condition [20]; our results for F + ε ∞ ren in these particular cases agree with the results in [19,20,21]. Note also that the Casimir effect with a quantized charged scalar matter field in the background of an external uniform magnetic field has been comprehensively analyzed in [30].…”

Influence of quantized massive matter fields on the Casimir effect

“…with parametrization Imu = sin ρ, Imv = cos ρ, employing only one selfadjoint extension parameter, ρ, [4]. The above restrictions ensure the selfadjointness of the Hamiltonian operator, H (0) , under the boundary condition taking explicitly the form…”

“…As was already mentioned, the expression for the induced vacuum energy per unit area of the boundary surface, see (35), can be regarded as purely formal, since it is ill-defined due to the divergence of infinite sums over l and n. To tame the divergence, a factor containing a regularization parameter should be inserted in (35). A summation over values of k l , which are determined by (20)-(22), is to be performed with the use of versions of the Abel-Plana formula, that were derived in [4,5,14,15]. According to these versions, a contribution of the boundaries is separated into a piece which is free from divergences, and, therefore, the regularization can be safely removed in this piece.…”