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(N-C) Yang-Mills theory and QCD. The magnetization and the corresponding effective cha rge are obtained from the effective Lagrangian. The renormalized Vacuu m magnetization will depend on the renormalization scale chosen. Regar dless of this, the effective charge decreasing with the magnetic held, as in QCD, corresponds to anti-screening and asymptotic freedom. In s pinor and scalar QED on the other hand, the effective charge is increa sing with the magnetic field, corresponding to screening. Including ef fects due to finite temperature and density, we comment on the effecti ve charge in a degenerate fermion gas, increasing linearly with the ch emical potential. Neglecting the tachyonic mode, we find that in hot Q CD the effective charge is decreasing as the inverse temperature, in f avor for the formation of a quark-gluon plasma. However, including the rear part of the contribution from the tachyonic mode, we find instea d an effective charge increasing with the temperature. Including a the rmal gluon mass, the effective charge in hot QCD is group invariant (u nlike in the two case above), and decreases logarithmically in accorda nce to the vacuum renormalization group equation, with the temperature as the momentum scale. (C) 1996 Academic Press, Inc.