  We discuss complete theory of spin-1/2 electron-positron quantum plasmas,
when electrons and positrons move with velocities mach smaller than the speed
of light. We derive a set of two fluid quantum hydrodynamic equations
consisting of the continuity, Euler, spin (magnetic moment) evolution equations
for each species. We explicitly include the Coulomb, spin-spin, Darwin and
annihilation interactions. The annihilation interaction is the main topic of
the paper. We consider contribution of the annihilation interaction in the
quantum hydrodynamic equations and in spectrum of waves in magnetized
electron-positron plasmas. We consider propagation of waves parallel and
perpendicular to an external magnetic field. We also consider oblique
propagation of longitudinal waves. We derive set of quantum kinetic equations
for electron-positron plasmas with the Darwin and annihilation interactions. We
apply the kinetic theory for the linear wave behavior in absence of external
fields. We calculate contribution of the Darwin and annihilation interactions
in the Landau damping of the Langmuir waves. We should mention that the
annihilation interaction does not change number of particles in the system. It
does not related to annihilation itself, but it exists as a result of
interaction of an electron-positron pair via conversion of the pair into
virtual photon. A pair of the non-linear Schrodinger equations for
electron-positron plasmas including the Darwin and annihilation interactions.
Existence of conserving helicity in electron-positron quantum plasmas of
spinning particles with the Darwin and annihilation interactions is
demonstrated. We show that annihilation interaction plays an important role in
quantum electron-positron plasmas giving contribution of the same magnitude as
the spin-spin interaction.
