  By introducing Dirac ?-function in superhigh magnetic field, we deduce a
general formula for pressure of degenerate and relativistic electrons, Pe,
which is suitable for superhigh magnetic fields, discuss the quantization of
Landau levels of electrons, and consider the quantum electrodynamic(QED)
effects on the equations of states (EOSs) for different matter systems. The
main conclusions are as follows: the stronger the magnetic field strength, the
higher the electron pressure becomes; compared with a common radio pulsar, a
magnetar could be a more compact oblate spheroid-like deformed neutron star due
to the anisotropic total pressure; and an increase in the maximum mass of a
magnetar is expected because of the positive contribution of the magnetic field
energy to the EOS of the star. Since this is an original work in which some
uncertainties could exist, to further modify and perfect our theory model
should be considered in our future studies.
