Electron conduction along quantizing magnetic fields in neutron star crusts. I. Theory

Transport properties of degenerate relativistic electrons along quantizing magnetic fields in neutron star crusts are considered. A kinetic equation is derived for the spin polarization density matrix of electrons. Its solution does not depend on the choice of basic electron wave functions unlike previous solutions of the traditional kinetic equation for the distribution function. The density matrix formalism shows that one can always reach high accuracy with the traditional method by a proper choice of the basic functions. Electron Coulomb scattering on ions is considered in liquid matter, and on high-temperature phonons or on charged impurities in solid matter. In the solid regime, the Debye -- Waller reduction of phonon scattering can strongly enhance the longitudinal thermal or electric conductivity. An efficient numerical method is proposed for calculating the transport properties of electron gas at any magnetic field of practical interest.