Employing the closed-time-path Green's function formalism (CTPGF), the electron selfenergy and vertex function at finite temperature are derived at one-loop level. The so-called "double termn" does not appear in our approach and thus, the unitarity of the theory is ensured automatically. The temperature-dependent mass and vertex corrections are dispersive due to the existence of electron-positron pair background. In the nonrelativistic limit, the explicit forms of shifts due to temperature of both mass and Lande's g factor are given, and their low temperature (T<>m) limits are discussed.
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