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Based on our previous work, we deduce a general formula for pressure ofdegenerate and relativistic electrons,Pe, which is suitable for superhighmagnetic fields, discuss the quantization of Landau levels of electrons, andconsider the quantum electrodynam-ic(QED) effects on the equations of states(EOSs) for different matter systems. The main conclusions are as follows:Pe isrelated to the magnetic field B, matter density ?, and electron fraction Ye ;the stronger the magnetic field, the higher the electron pressure becomes; thehigh electron pressure could be caused by high Fermi energy of electrons in asuperhigh magnetic field; compared with a common radio pulsar, a magnetar couldbe a more compact oblate spheroid-like deformed neutron star due to theanisotropic total pressure; and an increase in the maximum mass of a magnetaris expected because of the positive contribution of the magnetic field energyto the EOS of the star.

Pressure of Degenerate and Relativistic electrons in a superhigh magnetic field