Thermal scalar quantum field in static background gauge potentials
We study, at finite temperature, the energy-momentum tensor Tμμ(x) of a charged scalar field interacting with a static background electromagnetic field. Tμν separates into an UV divergent part Tseaμν representing the virtual sea, and an UV finite part Tplasmaμν describing the thermal plasma of the matter field. In the presence of a constant electric field E→, Tseaμν remains uniform while Tplasmaμν becomes spatially non-uniform in the direction of E→. A related (periodic) spatial non-uniformity is found for a constant static magnetic field B→ if one spatial direction perpendicular to B→ is compactified to a circle.