Duality in quark ferromagnetism

A self-consistent treatment of quark ferromagnetism is presented within the relativistic Hartree-Fock approximation. There appear various kinds of mean fields in the system, among which the axial-vector mean field is responsible to ferromagnetism. The ferromagnetic phase is further analyzed by the use of relativistic Stoner model, where the gluon propagator is replaced by a constant. The single-particle energies for two spin states of quarks exhibit the momentum-dependent exchange splitting, which in turn induces deformation of Fermi sea. These features resemble those in the pion-condensation theory. Actually, it is shown that there is a duality in the quark ferromagnetism in this model; it can be regarded as a pion condensed phase from another viewpoint. (author)