Dynamical Symmetry Breaking and Effective Lagrangians in U(n) Four-Fermion Models (n=2,3)

The formation of scalar condensates and dynamical symmetry breaking in the U(n) four-fermion models (for n=2,3) with two coupling constants has been studied by the functional integration method. The bosonization procedures of the models under consideration are performed in one loop approximation. The propagators of fermions, collective Bose-fields (bound states of fermions), as well as the mass formulas for the fermions and bosons, are found. It is shown that a self-consistent consideration of four-fermion models, in the framework of dimension regularization, provides the mass relations for fermions for the case $n\geq 3$. The effective Lagrangian of interacting scalar bosons is also derived for the case n=2.