We derive asymptotic freedom and the SU(3) Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian $H_s$, which is a matrix written in a basis that depend on the scale (or size) parameter s. The effective Hamiltonians $H_s$ and the (regularized) canonical Hamiltonian $H_0$ are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Date of publication:
EPJ Web Conf. 137 (2017) 03020