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