Asymptotic freedom and the infrared problem: A novel solution to the renormalization-group equations

The general solution to the renormalization-group equation is obtained by the method of characteristics. It is shown that the infrared limit can be calculated using the asymptotically free running coupling constant and that the result is highly sensitive to the presence of nonperturbative effects. The Landau-gauge gluon propagator is thereby shown to have a $\frac{1}{q^4}$ IR behavior indicative of confinement.