Conservation law in noncommutative geometry -- Application to spin-orbit   coupled systems
  The quantization scheme by noncommutative geometry developed in string theory is applied to establish the conservation law of twisted spin and spin current densities in the spin-orbit coupled systems. Starting from the pedagogical introduction to Hopf algebra and deformation quantization, the detailed derivation of the conservation law is given. 
Naoyuki Sugimoto and Naoto Nagaosa
math-ph cond-mat.mes-hall math.MP