In continuation of our earlier proposal [A. Das and J. Frenkel, Phys. Lett. B 680, 195 (2009).] and [A. Das and J. Frenkel, Phys. Rev. D 80, 125039 (2009).] for evaluating thermal effective actions, we determine the exact fermion propagator in $1+1$ dimensional massive QED. This propagator is used to derive the finite temperature effective action of the theory which generates systematically all the one loop Feynman amplitudes calculated in thermal perturbation theory. Various aspects of the effective action, including its imaginary part are discussed.

• Received 20 July 2010

DOI:https://doi.org/10.1103/PhysRevD.82.125002