  We present the first rigorous construction of the QFT Thirring model, for any
value of the mass, in a functional integral approach, by proving that a set of
Grassmann integrals converges, as the cutoffs are removed, to a set of
Schwinger functions verifying the Osterwalder-Schrader axioms. The massless
limit is investigated and it is shown that the Schwinger functions have
different properties with respect to the ones of the well known exact solution:
the Ward Identities have anomalies violating the anomaly non-renormalization
property and additional anomalies, apparently unnoticed before, are present in
the closed equation for the interacting propagator, obtained by combining a
Schwinger-Dyson equation with Ward Identities.
