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

摘要

The formation of scalar condensates and dynamical symmetry breaking in theU(n) four-fermion models (for n=2,3) with two coupling constants has beenstudied by the functional integration method. The bosonization procedures ofthe models under consideration are performed in one loop approximation. Thepropagators of fermions, collective Bose-fields (bound states of fermions), aswell as the mass formulas for the fermions and bosons, are found. It is shownthat a self-consistent consideration of four-fermion models, in the frameworkof dimension regularization, provides the mass relations for fermions for thecase $n\geq 3$. The effective Lagrangian of interacting scalar bosons is alsoderived for the case n=2.