Spinor Decomposition of SU(2) Gauge Potential and Spinor Structures of Chern–Simons and Chern Density

摘要

In this paper, the decomposition of SU(2) gauge potential in terms of Paulispinors is studied. Using this decomposition, the spinor strutures of theChern-Simons form and the Chern density are obtained. Furthermore, by thesespinor structures, the knot quantum number of non-Abelian gauge theory isdiscussed, and the second Chern number is characterized by the Hopf indices andthe Brouwer degrees of $phi $-mapping.