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arXiv · 1601.07801

Asymptocic Freedom of Gluons in Hamiltonian Dynamics

María Gómez-Rocha·Stanisław D. Głazek
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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 $β$-function coincides with the one obtained in an earlier calculation using a different generator.

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María Gómez-Rocha, Stanisław D. Głazek. 2016-01-28. Asymptocic Freedom of Gluons in Hamiltonian Dynamics. https://doi.org/10.1007/s00601-016-1078-0

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