  Correlation functions of fermionic fields described by the massless Thirring
model are analysed within the operator formalism developed by Klaiber and the
path-integral approach with massless fermions quantized in the chiral symmetric
phase. We notice that Klaiber's composite fermion operators possess
non-standard properties under parity transformations and construct operators
with standard parity properties. We find that Klaiber's parameterization of a
one-parameter family of solutions of the massless Thirring model is not well
defined, since it is not consistent with the requirement of chiral symmetry. We
show that the dynamical dimensions of correlation functions depend on an
arbitrary parameter induced by ambiguities of the evaluation of the chiral
Jacobian. A non-perturbative renormalization of the massless Thirring model is
discussed. We demonstrate that the infrared divergences of Klaiber's
correlation functions can be transferred into ultra-violet divergences by
renormalization of the wave function of fermionic fields. This makes Klaiber's
correlation functions non-singular in the infrared limit. We show that the
requirement of non-perturbative renormalizability of the massless Thirring
model fixes a free parameter of the path-integral approach. In turn, the
operator formalism is inconsistent with non-perturbative renormalizability of
the massless Thirring model. We carry out a non-perturbative renormalization of
the sine-Gordon model and show that it is not an asymptotically free theory as
well as the massless Thirring model. We calculate the fermion condensate by
using the Fourier transform of the two-point Green function of massless
Thirring fermion fields quantized in the chiral symmetric phase.
