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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 φ-mapping. PACS number(s): 11.15.−q, 02.40.−k Typeset using REVTEX Author to whom correspondence should be addressed. Electronic address: liuxin@lzu.edu.cn 1

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