Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in 2+1 Dimensions.

It is shown that in 2+1 dimensions,a constant magnetic field is a strong cata- lyst of dynamical flavor symmetry breaking,leading to generating a fermion dy- namical mass even at the weakest attractive interaction between fermions.The effect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field.The low-energy effective action in this model is derived and the thermodynamic pro- perties of the model are established.The relevance of this effect for planar condensed matter systems and for 3+1 dimensional theories at high temperature is pointed out.