On Gauge Theories with Additional Four-Fermion Interaction

In the ladder QED with four-fermion interaction, the anomalous dimension γ_m of the operator bar ψ ψ is calculated on the full critical line. It is shown that in the nonperturbative phase with the gauge coupling α⁽⁰⁾< α_c = π/3, the dynamical dimension d_{bar ψ ψ } =3 -γ _m is smaller than two (γ_m > 1) near the critical line. This suggests that gauge theories with fourfermion interaction may be renormalizable. The applications of these theories to the technicolor models are discussed.