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# Asymptotic freedom in the front-form Hamiltonian for quantum chromodynamics of gluons

Maria Gomez Rocha

Asymptotic freedom of gluons in QCD is obtained in the leading terms of their renormalized Hamiltonian in the Fock space. We calculate the three-gluon interaction term in the front-form Hamiltonian for gluons using the renormalization group procedure for effective particles (RGPEP). 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, $g_{\lambda}$, depending on the associated momentum scale $\lambda=1/s$, is calculated in the series expansion in powers of $g_0=g_{λ_0}$ up to the terms of third order, assuming some small value for $g_0$ at some large $\lambda_0$. The third-order QCD solution of the RGPEP equation to be discussed, provides an explicit example of how asymptotic freedom of gluons is exhibited in the scale-dependence of Hamiltonians as operators in the Fock space.