Magnetic permeability of the Dirac vacuum under confining boundary conditions

Abstract

We obtain the magnetic properties of the Dirac vacuum confined between two parallel plates. The confinement is implemented by MIT boundary conditions on the Dirac field and the properties are described by corrections to the Euler–Heisenberg effective Lagrangian. When the plates are separated by a distance in the range from nanometres to micrometres the new term associates with the vacuum a magnetic susceptibility of the same order of that of hydrogen or nitrogen at room temperature and atmospheric pressure.