Quantizing magnetic field and quark-hadron phase transition in a neutron star

We investigate the influence of a strong magnetic field on various properties of neutron stars with quark-hadron phase transition. The one-gluon exchange contribution in a magnetic field is calculated in a relativistic Dirac-Hartree-Fock approach. In a magnetic field of $5\times {10}^{18}$G in the center of the star, the overall equation of state is softer in comparison to the field-free case resulting in the reduction of maximum mass of the neutron star.