  We investigate a class of models in 1+1 dimensions with four fermion
interaction term. At each order of the perturbation expansion, the models are
ultraviolet finite and Lorentz non-invariant. We show that for certain
privileged values of the coupling constants, Lorentz symmetry is restored, and
indeed the model turns out to be conformally invariant. This phenomenon is both
quantum mechanical and non-perturbative.
