  Our aim is to study the electron-positron vacuum pressures in presence of a
strong magnetic field $B$. To that end, we obtain a general energy-momentum
tensor, depending on external parameters, which in the zero temperature and
zero density limit leads to vacuum expressions which are
approximation-independent. Anisotropic pressures arise, and in the tree
approximation of the magnetic field case, the pressure along $B$ is positive,
whereas perpendicular to $B$ it is negative. Due to the common axial symmetry,
the formal analogy with the Casimir effect is discussed, for which in addition
to the usual negative pressure perpendicular to the plates, there is a positive
pressure along the plates. The formal correspondence between the Casimir and
black body energy-momentum tensors is analyzed. The fermion hot vacuum behavior
in a magnetic field is also briefly discussed.
