Asymptotic Freedom from Thermal and Vacuum Magnetization

We calculate the effective Lagrangian for a magnetic field in spinor, scalar and vector QED. Connections are then made to SU(NC) Yang–Mills theory and QCD. The magnetization and the corresponding effective charge are obtained from the effective Lagrangian. The renormalized vacuum magnetization will depend on the renormalization scale chosen. In the absence of any natural scale, it is thus of little use to discuss diaor paramagnetic properties of the vacuum. When the vacuum susceptibility is decreasing (increasing) with the magnetic field as in QCD (spinor and scalar QED), the effective charge anyhow exhibits anti-screening and asymptotic freedom (screening). Including effects due to finite temperature and density, we comment on the effective charge in a degenerate fermion gas, increasing linearly with the chemical potential. Neglecting the tachyonic mode, we find that in hot QCD the effective charge is decreasing as the inverse temperature, in favor for the formation of a quarkgluon plasma. However, including the real part of the contribution from the tachyonic mode, we find instead an effective charge increasing linearly with the temperature. Comparisons (and some corrections) are made with previous results. Email address: [email protected]