  Solutions to the Thirring model are constructed in the framework of algebraic
QFT. It is shown that for all positive temperatures there are fermionic
solutions only if the coupling constant is $\lambda=\sqrt{2(2n+1)\pi}, n\in
{\bf N}$. These fermions are inequivalent and only for $n=1$ they are canonical
fields. In the general case solutions are anyons. Different anyons (which are
uncountably many) live in orthogonal spaces and obey dynamical equations (of
the type of Heisenberg's "Urgleichung") characterized by the corresponding
values of the statistic parameter. Thus statistic parameter turns out to be
related to the coupling constant $\lambda$ and the whole Hilbert space becomes
non-separable with a different "Urgleichung" satisfied in each of its sectors.
This feature certainly cannot be seen by any power expansion in $\lambda$.
Moreover, since the latter is tied to the statistic parameter, it is clear that
such an expansion is doomed to failure and will never reveal the true structure
of the theory.
  The correlation functions in the temperature state for the canonical dressed
fermions are shown by us to coincide with the ones for bare fields, that is in
agreement with the uniqueness of the $\tau$-KMS state over the CAR algebra
($\tau$ being the shift automorphism). Also the $\alpha$-anyon two-point
function is evaluated and for scalar field it reproduces the result that is
known from the literature.
