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

Source: [Dynamical renormalization group approach to the Altarelli-Parisi-Lipatov equations](<https://www.sota2.com/research/paper/68fa2deb1e209131ce85dcff>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T16:34:37.136Z

Authors: D. Boyanovsky, H. J. de Vega, D.-S. Lee, S.-Y. Wang, H.-L. Yu

Published: 2001-08-22T18:48:36.000Z

## Abstract

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 ln Q^2 corrections that arises 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-ph/0108180>)

[PDF](<https://arxiv.org/pdf/hep-ph/0108180.pdf>)