Spinor Decomposition of SU(2) Gauge Potential and The Spinor Structures of Chern-Simons and Chern Density
Yi-shi Duan, Xin Liu, Li-bin Fu
Abstract
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.
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