Chiral Properties of the QCD Vacuum in Ultra-Strong Magnetic Fileds: A Nambu-Jona -Lasinio Model with a Semi-Classical Approximation

The breaking of chiral symmetry of light quarks at zero temperature in the presence of strong quantizing magnetic field is studied using Nambu-Jona-Lasinio (NJL) model with a Thomas-Fermi type semi-classical formalism. It is found that the dynamically generated light quark mass can never become zero if the Landau levels are populated and increases with the increase of magnetic field strength.