The Boltzmann equation for a spinor distribution function with spinor momentum at the Fermi level

Abstract

Starting from a generalised Wigner distribution function with two momenta at the Fermi level, we obtain a spinor Boltzmann equation within the framework of Keldysh formalism. The additional terms that appear when there are two momenta disappear when the momenta are equal, and the two-momenta Boltzmann equation reduces to the one momentum case. We derive the quantum corrections for this spinor Boltzmann equation. When we take account of Planck’s constant in the gradient approximation used in the derivation of the Boltzmann equation, we find the spinor Boltzmann equation satisfied by the zeroth order distribution function, and we can naturally identify the first order quantum corrections. It is shown that the spin precession term appearing in the equation can be regarded as a quantum correction term in the zeroth order spinor Boltzmann equation.