  We study at finite temperature the energy-momentum tensor $T_{\mu\nu}(x)$ of
(i) a scalar field in arbitrary dimension, and (ii) a spinor field in 1+1
dimensions, interacting with a static background electromagnetic field.
$T_{\mu\nu}$ separates into an UV divergent part $T_{\mu\nu}^{sea}$
representing the virtual sea, and an UV finite part $T_{\mu\nu}^{plasma}$
describing the thermal plasma of the matter field. $T_{\mu\nu}^{sea}$ remains
uniform in the presence of a \underbar{uniform} electric field $\vec E$, while
$T_{\mu\nu}^{plasma}$ becomes a periodic function with period $\Delta x=2\pi
T/E$ in the direction parallel to $\vec E$. A related periodicity is found for
a uniform static magnetic field if one spatial direction perpendicular to the
magnetic field is compactified to a circle.
