Dynamical renormalization group approach to the Altarelli-Parisi-Lipatov equations

The Altarelli-Parisi-Lipatov equations for the parton distribution functions are rederived using the dynamical renormalization group approach to quantum kinetics. This method systematically treats the In Q(2) corrections that arise in perturbation theory as a renormalization of the parton distribution function and unambiguously indicates that the strong coupling must be allowed to run with the scale in the evolution kernel. To leading logarithmic accuracy the evolution equation is Markovian and the logarithmic divergences in the perturbative expansion are identified with the secular divergences (terms that grow in time) that emerge in a perturbative treatment of the kinetic equations in nonequilibrium systems. The resummation of the leading logarithms by the Altarelli-Parisi-Lipatov equation is thus similar to the resummation of the leading secular terms by the Boltzmann kinetic equation.