Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron (repost)

The measurements of the Hall coefficient RH and the Seebeck coefficient (thermoelectric power) S are known to give the sign of the carrier charge q. In sodium (Na) forming a body-centered cubic (bcc) lattice both RH and S are negative, indicating that the carrier is the "electron". In silver (Ag) forming a face-centered cubic (fcc) lattice the Hall coefficient RH is negative but the Seebeck coefficient S is positive. This complication arises from the Fermi surface of the metal. In conducting matter physics the "electrons" and the "holes" play important roles. The "electrons" ("holes") which by definition circulate counterclockwise (clockwise) around the magnetic field (flux) vector B cannot be discussed based on the prevailing equation of motion in the electron dynamics: dk/dt=q (E + v x B), k = k-vector, E = electric field, v = velocity since the energy-momentum relation is not incorporated in this equation. In this book we shall derive Newtonian equations of motion with a symmetric mass tensor. We diagonalize this tensor by introducing the principal masses and the principal axes of the inverse-mass tensor associated with the Fermi surface.