Quantum relativistic theory of the synchrotron/cyclotron radiation in a strongly-magnetized plasma: The case of longitudinal propagation

Full quantum relativistic treatment of the cyclotron/synchrotron emission and absorption in tenuous plasmas with superstrong magnetic field is developed for the case when the radiation wave-vector is parallel to the magnetic field. The emissivities and absorption coefficients for a plasma with arbitrary distribution function of particles are presented in terms of simple sums over the Landau levels. On the basis of these expressions, the negative absorption (maser amplification) is shown to be impossible for the longitudinal propagation in a tenuous plasma. The summation over the Landau levels is performed analytically, and the quantum effects are analysed in detail, for the thermal distribution of plasma particles. A new type of quantum relativistic oscillations is predicted in the emission and absorption spectra for a plasma with anisotropic temperature. The results obtained are useful for an interpretation of the X-ray and gamma-ray observations of the objects associated with strongly magnetized neutron stars (particularly of the gamma-ray bursters).