Two-dimensional QED approximation with allowance for finite temperature

Two-dimensional QED approximation is extended to the case of finite temperature. Using the proper-time Schwinger-Fock representation complemented by a procedure of temperature introducing, the authors calculate the temperature contribution into the Green function, polarization and mass operators and the contribution into the vertex function. Asymptotics of the expressions obtained in the high and low temperature limits are investigated. The Debye charge screening radius is obtained for the electron gas ground state in strong magnetic field. It is shown that the temperature correction to the mass operator is of the minus sign and it might compensate in the high temperature limit (and in the main logarithm approximation) the electron energy shift in the magnetic field. It is pointed out that similar situation takes place for the vertex function as well