  We consider the perturbation theory in the fermion mass (chiral perturbation
theory) for the two-dimensional quantum electrodynamics. With this aim, we
rewrite the theory in the equivalent bosonic form in which the interaction is
exponential and the fermion mass becomes the coupling constant. We reformulate
the bosonic perturbation theory in the superpropagator language and analyze its
ultraviolet behavior. We show that the boson Green's functions without vacuum
loops remain finite in all orders of the perturbation theory in the fermion
mass.
