Quarks and gluons in a magnetic field

Abstract

The quark gap equation under the rainbow truncation, with two versions of a phenomenological one-gluon exchange interaction and in the presence of a uniform magnetic field is considered. It is argued that in order to describe the quark condensate in the limit of vanishing magnetic fields, one must sum over the Landau levels. The resulting chiral quark condensate rises quadratically for small magnetic fields and linearly for large fields, in qualitative agreement with various recent lattice results. It is observed that when discussing quarks, the magnitude of the magnetic field must be considered relative to the scale of the strong interaction.