Self-adjointness and the Casimir effect with confined quantized spinor matter

TL;DR

This paper generalizes boundary conditions for confined spinor matter to ensure self-adjointness of the Dirac operator and investigates the magnetic field's effect on the Casimir force, revealing predominantly repulsive vacuum pressures.

Contribution

It introduces a new boundary condition framework for spinor fields ensuring self-adjointness and analyzes the magnetic field's impact on the Casimir effect with these conditions.

Findings

Casimir force is generally repulsive under studied conditions.

Boundary conditions ensuring self-adjointness are generalized.

Magnetic field influences vacuum pressure between plates.

Abstract

A generalization of the MIT bag boundary condition for spinor matter is proposed basing on the requirement that the Dirac hamiltonian operator be self-adjoint. An influence of a background magnetic field on the vacuum of charged spinor matter confined between two parallel material plates is studied. Employing the most general set of boundary conditions at the plates in the case of the uniform magnetic field directed orthogonally to the plates, we find the pressure from the vacuum onto the plates. In physically plausible situations, the Casimir effect is shown to be repulsive, independently of a choice of boundary conditions and of a distance between the plates.