In electron-positron plasmas some of the plasma modes are
decoupled due to the equal charge to mass ratio of both species. The dispersion
properties of the propagation of linear waves in degenerate electron–positron
magnetoplasma are investigated. By using the quantum hydrodynamic equations
with magnetic fields of the Wigner–Maxwell system, we have obtained a set
of new dispersion relations in which ions’ motions are not considered. The
general dielectric tensor is derived using the electron and positron densities
and its momentum response to the quantum effects due to Bohm potential
and the statistical effect of Femi temperature. It has been demonstrated the
importance of magnetic field and its role with the quantum effects in these
plasmas which support the propagation of electromagnetic linear waves.
Besides, the dispersion relations in case of parallel and perpendicular modes
are investigated for different positron-electron density ratios.