Dynamical symmetry breaking in a non-polynomial four-fermion model

We present a new four-fermion model with a strongly non-polynomial coupling. To eliminate these non-polynomialities, we introduce two auxiliary vector fields and show that the dynamical Lorentz symmetry breaking is possible in our theory, as revealed by the effective potential generated for these vector fields. We explicitly calculate the low-energy effective action for these fields, which is given by the sum of three Maxwell terms (one for each field and a mixed one) plus a potential term displaying nontrivial minima.