Two-dimensional approximation of QED with allowance for finite temperature

The two-dimensional approximation of quantum electrodynamics is generalized to the case of a finite temperature. The Schwinger–Fock proper-time representation, augmented by a procedure for introducing temperature, is used to find the temperature contribution to the Green's function, polarization operator, mass operator, and also the vertex function. The behavior of these expressions in the limits of high and low temperatures is found. The Debye charge screening radius for an electron gas in the ground state in a strong magnetic field is obtained. It is shown that for the mass operator the temperature correction has a negative sign and in the high-temperature limit may compensate (in the leading logarithmic approximation) the energy shift of an electron in a magnetic field. It is shown that an analogous situation obtains for the vertex function.