Vacuum polarization in thermal QED with an external magnetic field

The one-loop vacuum polarization tensor is computed in QED with an external, constant, homogeneous magnetic field at finite temperature. The Schwinger proper-time formalism is used and the computations are done in Euclidian space. The well-known results are recovered when the temperature and/or the magnetic field are switched off and the effect of the magnetic field on the Debye screening is discussed.