Asymptocic Freedom of Gluons in Hamiltonian Dynamics

TL;DR

This paper demonstrates asymptotic freedom of gluons within the Hamiltonian framework of Yang-Mills theory by employing the renormalization group procedure for effective particles, confirming the scale dependence of the coupling constant.

Contribution

It introduces a Hamiltonian-based derivation of gluon asymptotic freedom using RGPEP, aligning with previous results but within a different formalism.

Findings

The three-gluon vertex depends on the scale parameter s.

The Hamiltonian coupling exhibits asymptotic freedom.

The Hamiltonian β-function matches earlier calculations.

Abstract

We derive asymptotic freedom of gluons in terms of the renormalized $SU(3)$ Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles (RGPEP) to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of $g$ up to third order. The resulting three-gluon vertex is a function of the scale parameter $s$ that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian $\beta$-function coincides with the one obtained in an earlier calculation using a different generator.