Thermal scaler quantum field in static background gauge potentials

We study, at finite temperature, the energy-momentum tensor T-mu nu(x) of a charged scalar field interacting with a static background electromagnetic field. T-mu nu separates into an UV divergent part T-mu nu(sea) representin g the virtual sea, and an UV finite part T-mu nu(plasma) plasma of the matt er held. In the presence of a constant electric held (E) over right arrow, T-mu nu(sea) remains uniform while T-mu nu(plasma) becomes spatially non-un iform in the direction of (E) over right arrow. A related (periodic) spatia l non-uniformity is found for a constant static magnetic field (B) over rig ht arrow if one spatial direction perpendicular to (B) over right arrow is compactified to a circle.