Spin hall effect associated with SU(2) gauge field

In this paper, we focus on the connection between spin Hall effect and spin force. Here we investigate that the spin force due to spin-orbit coupling, which, in two-dimensional system, is equivalent to forces of Hirsch and Chudnovsky besides constant factors 3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{3}{2}$\end{document} respectively, is a part of classic Anandan force, and that the spin Hall effect is an anomalous Hall effect. Furthermore, we develop the method of AC phase to derive the expression for the spin force, and note that the most basic spin Hall effect indeed originate from the AC phase and is therefore an intrinsic quantum mechanical property of spin. This method differs from approach of Berry phase in the study of anomalous Hall effect , which is the intrinsic property of the perfect crystal. On the other hand, we use an elegant skill to show that the Chudnovsky-Drude model is reasonable. Here we have improved the theoretical values of spin Hall conductivity of Chudnovsky. Compared to the theoretical values of spin Hall conductivity in the Chudnovsky-Drude model, ours are in better agreement with experimentation. Finally, we discuss the relation between spin Hall effect and fractional statistics.