Shear electromagnetic waves in strongly magnetized quantum electron positron plasmas

We study the dispersion properties of low-frequency (in comparison with the electron/positron gyrofrequency) shear electromagnetic waves in an ultra-cold quantum magnetoplasma composed of electrons and positrons. By using the electron and positron fluid velocities deduced from the quantum momentum equations, together with the continuity equations and Ampère's law, we derive the governing equation for the shear waves. This equation is then Fourier transformed to obtain the dispersion relation, and to show the modification of the electromagnetic wave dispersions due to the electron and positron quantum effects. The latter can play a significant role in magnetic reconnection and in the formation of localized electromagnetic wave structures at quantum scales in ultra-cold quantum magnetoplasmas.