ELECTRICAL-CONDUCTIVITY OF NEUTRON-STAR CORES IN THE PRESENCE OF A MAGNETIC-FIELD .1. GENERAL-SOLUTION FOR A MULTICOMPONENT FERMI-LIQUID

General equations for the conductivity and resistivity tensors in a multicomponent plasma of strongly degenerate fermions with a magnetic field B are derived in terms of rates of momentum transfer in particle collisions. For two-, three-, and four-component plasmas, the equations are obtained in closed form. Scaling relations are presented which exhibit the universal temperature and magnetic field dependence of the conductivity and resistivity. When the magnetic field is high and an electrically neutral particle component is present, the resistivity transverse to B, R perpendicular-to, suffers an enhancement R perpendicular-to approximately B2. When the neutral component is absent, R perpendicular-to is field-independent as B --> infinity. The expressions for the momentum transfer rates are simplified for further application to the neutron star interiors in the next paper (this issue). The derivation of the expressions for the particle diffusion tensor is outlined in the Appendix.