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 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.
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Gómez-Rocha, M., Głazek, S.D. Asymptocic Freedom of Gluons in Hamiltonian Dynamics. Few-Body Syst 57, 509–513 (2016). https://doi.org/10.1007/s00601-016-1078-0
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DOI: https://doi.org/10.1007/s00601-016-1078-0