  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.
