Phase-space dynamics of semiclassical spin- 1/2 Bloch electrons

Following recent interest in a kinetic description of the semiclassical Bloch electron dynamics, we propose a new formulation based on the previously developed Lie-Poisson formulation of dynamics. It includes modifications required to account for the Berry curvature contribution to the electron's equation of motion as well as essential ingredients of a quantum treatment of spin- 1/2 degrees of freedom. Our theory is also manifestly gauge invariant and thus permits inclusion of the electron interactions. The scope of our formulation extends beyond its solid state physics motivation and includes recently discussed noncommutative generalizations of classical mechanics as well as historically important models from quantum gravity physics.