We compute the one-loop thermomagnetic corrections to the self-coupling in a model where charged scalars interact also with a constant magnetic field. The calculation is motivated by the possibility that the critical temperature for the chiral phase transition in a magnetic background can be influenced by the dependence of the coupling constant on the magnetic field. We show that the coupling decreases as a function of the field strength. This functional dependence introduces in turn a correction to the boson masses which causes the critical temperature to decrease as a function of the field strength.

We compute the quantum corrections to the gluon distribution function in the background of a non-Abelian Weizsäcker-Williams field. These corrections are valid to all orders in the effective coupling ${\mathrm{\alpha }}_{\mathit{s}}$μ, where ${\mathrm{\mu }}^2$ denotes the average valence quark color charge squared per unit area. We find ln(1/x) logarithmic corrections to the classical gluon distribution function. The one-loop corrections to the classical Weizsäcker-Williams field do not contribute to these singular terms in the distribution function. Their effect is to cause the running of ${\mathrm{\alpha }}_{\mathit{s}}$. © 1995 The American Physical Society.

We compute the critical temperature for the chiral transition in the background of a magnetic field in the linear sigma model, including the quark contribution and the thermomagnetic effects induced on the coupling constants at one-loop level. We show that the critical temperature decreases as a function of the field strength. The effect of fermions on the critical temperature is small and the main effect on this observable comes from the charged pions. The findings support the idea that the inverse magnetic catalysis phenomenon receives a contribution due only to chiral symmetry effects independent of the deconfinement transition.

We study the one-loop gluon polarization tensor at zero and finite temperature in the presence of a magnetic field, to extract the thermomagnetic evolution of the strong coupling ${\alpha }_s$. We analyze four distinct regimes, to wit, the small and large field cases, both at zero and at high temperature. From a renormalization group analysis, we show that at zero temperature, either for small or large magnetic fields, and for a fixed transferred momentum $Q^2$, ${\alpha }_s$ grows with the field strength with respect to its vacuum value. However, at high temperature and also for a fixed value of $Q^2$, we find two different cases. When the magnetic field is even larger than the squared temperature, ${\alpha }_s$ also grows with the field strength. On the contrary, when the squared temperature is larger than the magnetic field, a turnover behavior occurs, and ${\alpha }_s$ decreases with the field strength. This thermomagnetic behavior of ${\alpha }_s$ can help explain the inverse magnetic catalysis phenomenon found by lattice QCD calculations.

We carefully compute the gluon propagator in the background of a non-Abelian Weizsäcker-Williams field. This background field is generated by the valence quarks in very large nuclei. We find contact terms in the small fluctuation equations of motion which induce corrections to a previously incorrect result for the gluon propagator in such a background field. The well-known problem of the Hermiticity of certain operators in the light cone gauge is resolved for the Weizsäcker-Williams background field. This is achieved by working in a gauge where singular terms in the equations of motion are absent and then gauge transforming the small fluctuation fields to the light cone gauge.