Asymptocic Freedom of Gluons in Hamiltonian Dynamics

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.

Comments: 5 pages, 1 figure. Presented by María Gómez-Rocha at Light Cone 2015, 21-25 September, 2015, INFN Frascati National Laboratories