Negative Pressures and Energies in Magnetized and Casimir Vacua

Abstract

We study the electron-positron vacuum in a strong magnetic field $B$ in parallel with Casimir effect. Use is made of the energy-momentum tensor, taken as the zero temperature and zero density limit of the relativistic quantum statistical tensor. In both magnetic field and Casimir cases it is shown the arising of anisotropic pressures. In the first case the pressure transversal to the field $B$ is negative, whereas along $B$ an usual positive pressure arises. Similarly, in addition to the usual negative Casimir pressure perpendicular to the plates, the existence of a positive pressure along the plates is predicted. The anisotropic pressures suggests a flow of the virtual particles in both cases. By assuming regions of the universe having random orientation of the lines of force, cosmological consequences are discussed in the magnetic field case.