Renormalization group and dynamical symmetry breakdown in Abelian gauge theories

Generalized renormalization group equations are used to analyze the dynamical mechanism of particle mass generation in terms of the Cornwall-Norton model both with and without cut-off. Solutions which contain non-zero physical masses of the two fermions (m1m2) and of one of the vector bosons (μ) when the bare masses msub(1Λ), msub(2Λ), μsub(Λ), approach zero are looked for. For a theory without cut-off results are obtained which are similar to those of Cornwall. For a theory with cut-off the mass generation mechanism may only occur when a bare coupling constant αsub(Λ) of the Asub(μ) vector boson, which remains massless, exceeds some critical value αsub(c). In this case the fermion masses turn out to be of the superconductivity type. (Auth.)