Chiral phase transitions in an external field

A formalism is described for the study of chiral symmetry breaking in the presence of a constant external field. It is applied to the case of a uniform magnetic field and chiral symmetry is found to be spontaneously broken in the weak coupling regime. The broken chiral symmetry is restored at high tempeatures as well as at large chemical potentials, but with different characteristics: the chiral symmetry restoration at high temperatures corresponds to a second-order phase transition, whereas the chiral phase transition at high densities is a first-order one.